"I understand that the older paper you link to requires the metric to be standard near the critical points. But my understanding is that the more recent paper linked to in the question (front.math.ucdavis.edu/1102.2838) is precisely meant to address the case of an arbitrary metric. Qin says so explicitly in the abstract." front.math.ucdavis.edu/0403.5496." front.math.ucdavis.edu/0407.5468, while the AMS Bulletin articles are all freely available online through the AMS webpage. The third paper is older, with access depending entirely on local libraries." front.math.ucdavis.edu/0601.5305. The paper I think appeared in Topology." front.math.ucdavis.edu/0710.4561 ." front.math.ucdavis.edu/0805.1398" front.math.ucdavis.edu/1005.3895 I have a different theory as to why ""IV"" never came out- that understanding the relationship of the Aarhus integral with the Ohtsuki series is a harder problem which requires more techniques, and the authors might not have fully appreciated that at the time ""I"" was written. I'm very happy that it's done now!" front.math.ucdavis.edu/1007.3606" front.math.ucdavis.edu/1009.5018 " http://front.math.ucdavis.edu/0001.5063, which is a paper of Krushkal-Quinn ""Subexponential groups in 4-manifold topology"". I gather you are not satisfied with their approach, would you explain why not?" http://front.math.ucdavis.edu/0006.5018" http://front.math.ucdavis.edu/0010.5077" http://front.math.ucdavis.edu/0010.5163, ordinary triple point is used in the sense I mentioned. The only case that satisfies both definitions is a singularity of type $A_1$, since the cone over $C_n$ is not a Gorenstein singularity for $n>2$. I think both definitions exist in the literature." http://front.math.ucdavis.edu/0010.5184 but with Leeb replacing Maillot in the author list. " http://front.math.ucdavis.edu/0102.5020" http://front.math.ucdavis.edu/0103.5009 might be; our paper David references is about subwords whose Demazure product is $x$, instead of the actual product, as in the question." http://front.math.ucdavis.edu/0106.5063" http://front.math.ucdavis.edu/0107.5011" http://front.math.ucdavis.edu/0109.5183 for the homotopy classification of diffeomorphism groups of open surfaces." http://front.math.ucdavis.edu/0111.3053" http://front.math.ucdavis.edu/0111.5043)." http://front.math.ucdavis.edu/0202.5001" http://front.math.ucdavis.edu/0203.5262 . It is mentioned at the bottom of page 2 and the top of page 5. Actually on page 5 a slightly stronger version that we needed is mentioned and maybe your method apply there too." http://front.math.ucdavis.edu/0204.5106" http://front.math.ucdavis.edu/0204.5275 http://front.math.ucdavis.edu/0208.5237 for an example of a finitely presented monster, and for a discussion why they are hard to come by. " http://front.math.ucdavis.edu/0211.5044 . For the former, AFAIK no one has a convincing analogue of the Jones polynomial. Milnor invariants can be interpreted and the Alexander polynomial is supposed to be related to Iwasawa theory (http://arxiv.org/abs/0904.3399v1), but I believe there's no good analogue of finite-type invariants with more loops." http://front.math.ucdavis.edu/0211.5378 http://front.math.ucdavis.edu/0309.5187" http://front.math.ucdavis.edu/0310.5381)." http://front.math.ucdavis.edu/0401.5075 It's very close in spirit with your line of inquiry. " http://front.math.ucdavis.edu/0401.5401 http://front.math.ucdavis.edu/0404.5350 which essentially suggests (quelle surprise) that to approach the Riemann hypothesis using these ideas would require considerable modification !" http://front.math.ucdavis.edu/0407.5422 http://front.math.ucdavis.edu/0407.5422" http://front.math.ucdavis.edu/0407.5438 http://front.math.ucdavis.edu/0409.5190 and http://front.math.ucdavis.edu/0409.5278 http://front.math.ucdavis.edu/0411.5469 has a proof which is particularly careful about these field of definition issues. But this sort of uncertainty is why I wasn't willing to completely commit to my answer." http://front.math.ucdavis.edu/0412.5078 http://front.math.ucdavis.edu/0412.5214 http://front.math.ucdavis.edu/0502.5144 ." http://front.math.ucdavis.edu/0503.5040 ), and as far as I remember, they consider the eigenvalues. At least that's some beginning." http://front.math.ucdavis.edu/0503.5040" http://front.math.ucdavis.edu/0503.5040." http://front.math.ucdavis.edu/0503.5054 http://front.math.ucdavis.edu/0504.5425." http://front.math.ucdavis.edu/0505.5634" http://front.math.ucdavis.edu/0506.5572" http://front.math.ucdavis.edu/0506.5578." http://front.math.ucdavis.edu/0508.5272 and http://front.math.ucdavis.edu/0509.5648 contains some results about $\sum k^rC_k$ mod p which may help." http://front.math.ucdavis.edu/0601.5305" http://front.math.ucdavis.edu/0602.5215 and my recent survey http://front.math.ucdavis.edu/0602.5539" http://front.math.ucdavis.edu/0602.5626" http://front.math.ucdavis.edu/0604.5399" http://front.math.ucdavis.edu/0605.5067 (section 2). If lambda is bigger than kappa then there is a problem.... we do have Cohen like things (Remark 2.19 mentioned before) but I am not sure how we may add Laver/Miller reals with suitable properness" http://front.math.ucdavis.edu/0605.5069 In particular $Emb(\mathbb R, \mathbb R^3)$, denoted $\mathcal K_{3,1}$ in the above paper, all the path components are $K(\pi,1)$-spaces. The fundamental groups of the components are described in the 2nd paper James cites, and in the paper I cite. My new preprint on the ""splicing operad"" has a more uniform and geometric description." http://front.math.ucdavis.edu/0605.5553. In fact, I seem to recall that Minasyan-Osin showed that any countable group can be realized as Out(G) where G has property (T), but I cannot find a reference at the moment." http://front.math.ucdavis.edu/0606.5063 http://front.math.ucdavis.edu/0606.5220" http://front.math.ucdavis.edu/0606.5381 is what you want. The moves they work out are for 2-parameter families of knot/link diagrams in $S^1 \times D^2$ but it's a nice example of how the Thom-Mather theory works and I think there's little you have to do to adapt it for links in $\mathbb R^3$ -- I believe Fiedler essentially explains this in his paper. " http://front.math.ucdavis.edu/0606.5381" http://front.math.ucdavis.edu/0607.4021 where he argues that many of theorems about quantum computers are very sensitive to the model of random noise which is used, and would be false under different models. It is hardly surprising that he would be interested in knowing what noise is like in the real world." http://front.math.ucdavis.edu/0607.5513 http://front.math.ucdavis.edu/0608.5491 for a survey of the literature. " http://front.math.ucdavis.edu/0608.5752" http://front.math.ucdavis.edu/0610.5573" http://front.math.ucdavis.edu/0611.5118 for arguments of this type. The point is that a sequence of geodesics in the original metric space yields a geodesic in the ultralimit. " http://front.math.ucdavis.edu/0612.5085" http://front.math.ucdavis.edu/0612.5803 and the REU websites are at http://www.mtholyoke.edu/acad/math/past_projects.html I do recommend extra care be taken with any of the project papers...I remember finding mistakes in some of the older ones I read, and I vaguely remember looking back at my own a year later and being rather embarrassed by it..." http://front.math.ucdavis.edu/0701.5361" http://front.math.ucdavis.edu/0701.5365 . " http://front.math.ucdavis.edu/0701.5389." http://front.math.ucdavis.edu/0704.3749 http://front.math.ucdavis.edu/0705.3614) relates j and E_p-1 for all the p such that there is only one supersingular curve. i haven't been make that method work for p=11, and so i was hoping to do some explicit computer calculations to see if that might give some sort of hint as how to proceed..." http://front.math.ucdavis.edu/0705.4571" http://front.math.ucdavis.edu/0707.1144" http://front.math.ucdavis.edu/0707.3091. This problem is somewhat poisoned as many talented people thought hard of it with little or no progress." http://front.math.ucdavis.edu/0707.4231. One can probably also prove this for graphs, possibly with some extra conditions on the graph, such as bounded valence. " http://front.math.ucdavis.edu/0709.0101 http://front.math.ucdavis.edu/0709.1291" http://front.math.ucdavis.edu/0801.0261, http://front.math.ucdavis.edu/0805.2574" http://front.math.ucdavis.edu/0805.4418" http://front.math.ucdavis.edu/0805.4423 and http://front.math.ucdavis.edu/0806.1033>here http://front.math.ucdavis.edu/0807.4891" http://front.math.ucdavis.edu/0808.3351. http://front.math.ucdavis.edu/0809.1203 which I was not aware of." http://front.math.ucdavis.edu/0809.3976. http://front.math.ucdavis.edu/0810.1747 contains a covariant version of simplicial de Rham theory, with good categorical properties. I wrote it with applications to model structures in mind, although no such applications are actually in the paper." http://front.math.ucdavis.edu/0810.2336." http://front.math.ucdavis.edu/0810.2830" http://front.math.ucdavis.edu/0811.2080. But it's difficult if not impossible to fit all ""Kazhdan-Lusztig conjectures"" into one package. Different settings pose different technical challenges. " http://front.math.ucdavis.edu/0811.2482" http://front.math.ucdavis.edu/0812.0822 (and the paper itself was published in 2011 in the Munster Math. J., probably not different from the arXiv preprint). Also, the longer paper by Proctor is freely available online here: https://www-sciencedirect-com.silk.library.umass.edu/science/article/pii/S0021869384710647?via%3Dihub" http://front.math.ucdavis.edu/0901.1587 and http://front.math.ucdavis.edu/0901.4663" http://front.math.ucdavis.edu/0902.0648) but they are probably not quite what you want." http://front.math.ucdavis.edu/0902.3464 (""Universal covering spaces and fundamental groups in algebraic geometry as schemes"")." http://front.math.ucdavis.edu/0902.3464 (although opinions on what we did may vary)." http://front.math.ucdavis.edu/0902.4252 for a bit more info." http://front.math.ucdavis.edu/0904.1370 to get an idea what it takes to classify the smooth structure set for the product of only two spheres; classifying smooth manifolds in that structure set is even harder. " http://front.math.ucdavis.edu/0904.3350" http://front.math.ucdavis.edu/0904.3740?" http://front.math.ucdavis.edu/0904.4713 where it is needed to understand LG models associated to isolated hypersurface singularities. It elaborates on Tyler's comment." http://front.math.ucdavis.edu/0905.0290" http://front.math.ucdavis.edu/0905.1675" http://front.math.ucdavis.edu/0906.0045 ?" http://front.math.ucdavis.edu/0906.5193 http://front.math.ucdavis.edu/0907.0061" http://front.math.ucdavis.edu/0907.2444 http://front.math.ucdavis.edu/0909.3292 with mod-p done by Guerra (published at AGT) and and for $A_n$ mod-two http://front.math.ucdavis.edu/0909.4625" http://front.math.ucdavis.edu/0909.4844, contains a good account of the (almost) current state of knowledge. It also gives a good explanation of what cyclotomic Hecke algebras have to do with anything." http://front.math.ucdavis.edu/0911.3599" http://front.math.ucdavis.edu/1001.0897" http://front.math.ucdavis.edu/1001.2282 was not mentioned." http://front.math.ucdavis.edu/1001.2562 http://front.math.ucdavis.edu/1001.2719." http://front.math.ucdavis.edu/1001.4323]." http://front.math.ucdavis.edu/1003.5250 http://front.math.ucdavis.edu/1004.3908" http://front.math.ucdavis.edu/1005.4135 http://front.math.ucdavis.edu/1007.2777 http://front.math.ucdavis.edu/1007.2777 (and my earlier note is online here: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pjm/1102991730). Concerning linear reductivity of representations for reductive groups in characteristic 0, there are numerous references." http://front.math.ucdavis.edu/1008.1368. The closely related case of $F(\mathbb{P}^1,n)$ will appear soon." http://front.math.ucdavis.edu/1008.3868 Thanks again!" http://front.math.ucdavis.edu/1008.3868" http://front.math.ucdavis.edu/1008.3868) that Thompson group is not amenable, although personally I voted several times for amenability. But there are amenable groups whose Følner functions grow faster than any iterated exponent. See Erschler, Anna http://front.math.ucdavis.edu/1009.2823?" http://front.math.ucdavis.edu/1009.4364 ? They study subgroups of Abelian-by-cyclic groups. " http://front.math.ucdavis.edu/1010.1448 and references therein. http://front.math.ucdavis.edu/1010.3496 ." http://front.math.ucdavis.edu/1010.4101 " http://front.math.ucdavis.edu/1011.1691" http://front.math.ucdavis.edu/1011.3243) there is the $(\infty,1)$-category of spans, which is an example of a rather different flavour from the ones that you mention." http://front.math.ucdavis.edu/1011.3705 section 3.4." http://front.math.ucdavis.edu/1012.1325 in Bull. Math. Sciences. " http://front.math.ucdavis.edu/1012.1325, Section 3.2. " http://front.math.ucdavis.edu/1012.2021" http://front.math.ucdavis.edu/1012.3643" http://front.math.ucdavis.edu/1012.3643" http://front.math.ucdavis.edu/1101.3216" http://front.math.ucdavis.edu/1101.3733" http://front.math.ucdavis.edu/1102.0821" http://front.math.ucdavis.edu/1102.4901" http://front.math.ucdavis.edu/1103.0570" http://front.math.ucdavis.edu/1103.3423) discussed the Kolmogorov-Barzdin paper at great length. It is pretty clear that they (KB) DID NOT prove the Pinsker results, but something closer to the usual trivial ""a random bipartite graph is random"" result. I think it is not very nice to give credit where it is not due (and take away credit from Pinsker, who proved the foundational result in the field)." http://front.math.ucdavis.edu/1103.3873. I wanted to know if anybody before G. Yu formulated the question. I needed the answer for that paper. " http://front.math.ucdavis.edu/1104.1882" http://front.math.ucdavis.edu/1105.0865 and http://front.math.ucdavis.edu/1105.1970 ." http://front.math.ucdavis.edu/1105.4824)." http://front.math.ucdavis.edu/1105.5500" http://front.math.ucdavis.edu/1106.1601 If I understand correctly the finite field analogs still have Behrend-like bounds so not bounds of the form $(p-t)^n$ for t>0." http://front.math.ucdavis.edu/1106.3066 (there's a video talk by Yamazaki at the Simons Institute). It computes the volume of punctured torus bundles in terms of the trace of an action on quantum Teichmuller space. It's not clear to me if this is related to the WRT invariants, but maybe there is a connection via work of Bonahon et al., eg: http://front.math.ucdavis.edu/1106.4595" http://front.math.ucdavis.edu/1106.4789" http://front.math.ucdavis.edu/1107.1707)" http://front.math.ucdavis.edu/1107.1813 http://front.math.ucdavis.edu/1107.2843, for example, or http://front.math.ucdavis.edu/1107.3377 and I noticed many probabilities are expanded in powers of $\frac{1}{\pi}$ and I wondered what that was about. They seem to be counting frequencies of ""motifs"" (for lack of a better word) in uniform spanning trees. I came up with the $1 \times 1 \times n$ problem to try to understand this better." http://front.math.ucdavis.edu/1108.1776 ""Subword complexes, cluster complexes, and generalized multi-associahedra"" and then to geometry in http://front.math.ucdavis.edu/1109.5150 http://front.math.ucdavis.edu/1110.0818 may be relevant." http://front.math.ucdavis.edu/1110.0818." http://front.math.ucdavis.edu/1110.1940" http://front.math.ucdavis.edu/1110.5008. I think the point is that if one only cares about group theoretic conclusions (e.g. that a certain fundamental group is virtually nilpotent), then one can ignore the space where the local preudogroup acts and focus on suitable group theoretic data." http://front.math.ucdavis.edu/1110.5027 http://front.math.ucdavis.edu/1110.6263. I just asked him to define the sandpile model not for an infinite graph but for a sequence of finite graphs converging to an infinite graph. This way there is not ambiguity. " http://front.math.ucdavis.edu/1110.6374" http://front.math.ucdavis.edu/1111.3603" http://front.math.ucdavis.edu/1111.4338" http://front.math.ucdavis.edu/1111.5146." http://front.math.ucdavis.edu/1112.0739 for information on all known counter-examples." http://front.math.ucdavis.edu/1112.0845" http://front.math.ucdavis.edu/1112.2367" http://front.math.ucdavis.edu/1201.3129 where a weaker genericity result is proven in dimension 3. " http://front.math.ucdavis.edu/1202.1856 for a paper by Everitt, Lipshitz, Sarkar, and Turner comparing two such constructions for an example." http://front.math.ucdavis.edu/1202.2250 )." http://front.math.ucdavis.edu/1202.2724" http://front.math.ucdavis.edu/1202.2724" http://front.math.ucdavis.edu/1203.0596" http://front.math.ucdavis.edu/1204.4242" http://front.math.ucdavis.edu/1205.0515)." http://front.math.ucdavis.edu/1205.1209" http://front.math.ucdavis.edu/1205.6343) by K. M. Frahm, A. D. Chepelianskii, D. L. Shepelyansky ?" http://front.math.ucdavis.edu/1207.0724" http://front.math.ucdavis.edu/1207.0896." http://front.math.ucdavis.edu/1207.2364. Sorry for the advertisement." http://front.math.ucdavis.edu/1209.0640 " http://front.math.ucdavis.edu/1209.5124. To make things even harder this conjecture, well theorem, only applies to regular holonomic D-modules. I have not heard of any proposed conjecture for non-holonomic D-modules..." http://front.math.ucdavis.edu/1211.3692. Given the simple groups in (2), I also don't see how to recover (1) by group theory alone." http://front.math.ucdavis.edu/1301.0873 (Also, can you say something about why this should be relevant to the question?)" http://front.math.ucdavis.edu/1301.3222." http://front.math.ucdavis.edu/1304.3730 shows that in every dimension ≥6 there exists a closed aspherical manifold that is not homeomorphic to a simplicial complex." http://front.math.ucdavis.edu/1305.0052 http://front.math.ucdavis.edu/1305.6083." http://front.math.ucdavis.edu/1307.5115 where (as far as I can see) he shows in the proof of Theorem 1, that a genus one knot can not have an immersed Seifert surface of genus one with a homologically non-trivial curve. This seems to fit nicely with your answer, you `need some space' to get such immersed Seifert surfaces." http://front.math.ucdavis.edu/1309.0043. My experience is that negativity of the curvature does not really give you much benefit, which is why most sources treat the nonpositively curved case. The condition $K<0$ is easy to check but hard to work with, as I explain in the survey." http://front.math.ucdavis.edu/1309.6539 for a recent partial result." http://front.math.ucdavis.edu/1310.1159" http://front.math.ucdavis.edu/1312.2198" http://front.math.ucdavis.edu/1404.4671 ""Brick manifolds and toric varieties of brick polytopes""." http://front.math.ucdavis.edu/1404.5559 http://front.math.ucdavis.edu/1404.7630 (their interest is more general, but the discussion is useful even in the ""classical"" case)." http://front.math.ucdavis.edu/1405.3479 !" http://front.math.ucdavis.edu/1406.3607 which claims to prove the conjecture (and seems serious on first look)." http://front.math.ucdavis.edu/1406.4217 (note Remark 2.19 there). For preservation of bounding properties I would check http://front.math.ucdavis.edu/1407.4711" http://front.math.ucdavis.edu/1410.1358 http://front.math.ucdavis.edu/1410.7089 , especially Th. C and Cor. D." http://front.math.ucdavis.edu/1501.00300 for more recent works." http://front.math.ucdavis.edu/1502.05770" http://front.math.ucdavis.edu/1503.04070" http://front.math.ucdavis.edu/1503.06762); but note in Problem 10(a) that they don't really mean ""lower bound""." http://front.math.ucdavis.edu/1509.01887 contains a simple counterexample to my (corrected) question: the triangle with vertices $(0,0)$, $(\alpha,0)$, and $(0,1/\alpha)$, where $\alpha = \frac 12(3+\sqrt{5})$." http://front.math.ucdavis.edu/1602.07276" http://front.math.ucdavis.edu/1605.01721, and article by Tits is at http://www.sciencedirect.com/science/article/pii/002186939090201X" http://front.math.ucdavis.edu/1705.01141" http://front.math.ucdavis.edu/1705.05083 and his references." http://front.math.ucdavis.edu/1709.05776) which treats invariants in triple tensor products. These papers show that the GHKK theory applies to the representation theoretic situations. However, they don't give any description of the resulting bases or the scattering diagrams." http://front.math.ucdavis.edu/1805.00815 , which connects rowmotion to representation theory." http://front.math.ucdavis.edu/1902.10334 and http://front.math.ucdavis.edu/1903.00551" http://front.math.ucdavis.edu/1905.08460), our computations suggest that perhaps the MV basis coincides with the GHKK basis." http://front.math.ucdavis.edu/1907.01155" http://front.math.ucdavis.edu/1910.00960" http://front.math.ucdavis.edu/9509.5228 and then look at http://front.math.ucdavis.edu/9511.5213" http://front.math.ucdavis.edu/9707.5232, but **not** clicking on the .pdf link on that page. Click on the .ps link instead. That's what I needed to do on my machine." http://front.math.ucdavis.edu/9801.5019, http://front.math.ucdavis.edu/9801.5045, http://front.math.ucdavis.edu/9801.5058" http://front.math.ucdavis.edu/9801.5119" http://front.math.ucdavis.edu/9803.5150) referred to is ""Universality theorems for configuration spaces of planar linkages"", Topology 41 (2002), no. 6, 1051–1107. I've added a link to that paper in the answer." http://front.math.ucdavis.edu/9810.5017" http://front.math.ucdavis.edu/9907.5073 A pleasant feature of his construction is that it works for any topological monoid, and the ""geometric picture"" of an element of EG, BG, is very explicit. " http://front.math.ucdavis.edu/9908.5012 http://front.math.ucdavis.edu/9908.5012" http://front.math.ucdavis.edu/9911.5050 2. I agree, but you presented both as set-theoretic or topological quotients." http://front.math.ucdavis.edu/9912.5088 Most of the parts will go through unchanged, but we'd need to figure out the equivariant version of (*)." http://front.math.ucdavis.edu/about , although the physics committee there is not current)." http://front.math.ucdavis.edu/categories/math" http://front.math.ucdavis.edu/categories/math) or to the advisory committee (see http://front.math.ucdavis.edu/math.CO/0601431 For the added names: of course (also I only had some quite specific developpment in mind, not a general list for AddComb). " http://front.math.ucdavis.edu/math.HO/0510054" http://front.math.ucdavis.edu/math.LO/0311165 (there is an exposition in section 1G of http://www.math.wisc.edu/~keisler/foundations.html)." http://front.math.ucdavis.edu/math.LO/9502230) of Shelah and Zapletal is of some relevance." http://front.math.ucdavis.edu/math.LO/9607227), but it seems to me that this is quite different from our paper. Our forcings are not ccc, and our forcing looks more like a product than an iteration, in the sense that there is no obvious linear order on the coordinates; each ""iterand"" produces a real which is somewhat generic over all the others. Also (bug or feature?) we do not increase $\mathfrak d$. At the moment." http://front.math.ucdavis.edu/math.NT/0305421"">my paper with S. Robins and S. Zacks)." http://front.math.ucdavis.edu/math/0209256) of Greg's." http://front.math.ucdavis.edu/math/0405366" http://front.math.ucdavis.edu/math/9802040, so that gives examples." http://front.math.ucdavis.edu/search?a=%28morrison+snyder%29&t=&q=&c=&n=25&s=Listings" http://front.math.ucdavis.edu/search?a=&t=&q=Lie+superalgebra+%2B+character&c=&n=25&s=Listings" http://front.math.ucdavis.edu/search?a=&t=chow+quotients+of+grassmannians" http://front.math.ucdavis.edu/search?a=braden+proudfoot+webster . Ben Webster will probably point you to which of his talks http://people.virginia.edu/~btw4e/talks.html goes into most detail about the quiver/Yangian case." http://front.math.ucdavis.edu/search?a=de+graaf-w&t=&q=&c=&n=25&s=Listings !!" http://front.math.ucdavis.edu/search?a=de+graaf-w&t=&q=&c=&n=25&s=Listings" http://front.math.ucdavis.edu/search?a=howe-roger&t=&q=&c=&n=25&s=Listings They're based on the $GL(m)\times T^n$ action on ${\mathbb A}^{mn}$, not quite Schur-Weyl duality, but I still expect it should generalize to generic $q$." http://front.math.ucdavis.edu/search?a=knutson&t=polygon" http://front.math.ucdavis.edu/search?a=knutson&t=polygon"