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Is this question acceptable?: Mapping class group and property (T)

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  1.  
    • CommentAuthorHJRW
    • CommentTimeFeb 2nd 2012
     

    There has been a little discussion in comments of whether this question should be closed. I'm starting this this meta thread to accommodate such discussion.

    Note that similar issues were discussed in this thread.

    My opinion is that this question is fine, for roughly the same reasons as I gave in the previous thread.

  2.  

    A priori I think the question is fine, as you could imagine there being an answer along the lines of "The paper in preparation called X in the bibliography is now called Y, and the proof of Theorem 5 appears on page Z." But since such an answer hasn't appeared I feel like this question is going to do more harm than good, and should be closed. It sounds like something that would be better handled privately.

    • CommentAuthorquid
    • CommentTimeFeb 2nd 2012 edited
     

    I interpret the author's answer as indirect evidence that there is not interest in a public discussion on MO. Thus I vote to close.

  4.  

    I agree with Noah and quid. There's nothing wrong with the original question, but if Andersen doesn't want to have a public discussion on MO about the proof then he should not be pressured to do so. I will also vote to close.

    • CommentAuthormarkvs
    • CommentTimeFeb 3rd 2012
     
    I do not see much difference between the paper by Shavgulidze on Thompson's group and the paper by Andersen on the mapping class group. Both authors are specialists in quantum mathematical physics, and number 5 seems to play the same role in both papers (Lemma 5 in Shavgulidze's paper was wrong). The question is much more important than the question about Thompson's group since people (including myself) frequently refer to Andersen's paper. So I voted to reopen the question. I do not expect new answers but perhaps the author will respond to the comments. Truth, the question does not need to be open for that, but psychologically it is harder to comment on closed questions.
    • CommentAuthorquid
    • CommentTimeFeb 3rd 2012
     

    @markvs: but the author already replied to your comment, via an edit to the question adding something like 'including theorem 5'. Actually this non-answer to your comment was my main motivation to close.

    (In general I am in favor of such questions and argued in favor of them on other occassions; I am also not very much 'against' this one, but due to the involvement of the author the situation is a bit different IMO in this case.)

    • CommentAuthormarkvs
    • CommentTimeFeb 3rd 2012 edited
     
    @quid: You are right that the question is different because the author is involved. But this actually makes the question much more useful. If, for example, Shavgulidze answered the Thompson group question, it would be very nice (he knew about the discussion but chose not to get involved). The statement that a proof "exists" is not very satisfactory (say, for the references) because the main question remains: where is the proof? As the OP says, there are rumors and speculations around this paper which need to be resolved, and it is not because of simple curiosity. Some serious math depends on it. For example, if the proof actually exists plus if, as Andersen expected (but did not claim explicitly), all subgroups of the mapping class group do not have property (T), then one of our results (with Behrstock and Drutu), and several other results become redundant. Now all these results hang in the air.
  8.  

    I think you should ask Jorgen over email. He may be more inclined to discuss it there. If he wanted to say something publicly here, he would have already.

    • CommentAuthormarkvs
    • CommentTimeFeb 3rd 2012 edited
     
    @Noah: I have done it and received exactly the same (non-)answer about a year ago.
  10.  

    "I have done it and received exactly the same (non-)answer about a year ago." Well then I don't know what you hope to accomplish here.

    If the question is reopened I will vote to close.

    • CommentAuthormarkvs
    • CommentTimeFeb 4th 2012
     
    @Tom: I hope to accomplish either a more complete answer like the info about the exact location of the proof which "exists" and who are the authors of the "existing" proof or a clear evidence that the proof does not in fact exist (if the answer is not given). Both options will stop rumors and speculations because one can refer to MO (which is a public enough place as opposite to the private email correspondence) as evidence. So far the second option prevails. Yes, of course you are free to vote to close. As I said, it does not really matter whether the question is closed or open.
  12.  
    @markvs : I think that Joergen has made it clear that he does not want to discuss the details of this on MathOverflow. I think that as a matter of policy, we should not have these kinds of discussions of people's work on MathOverflow if they do not want it here.
    • CommentAuthormarkvs
    • CommentTimeFeb 4th 2012
     
    @Andy: It is not quite so. If Joergen did not want to discuss it on MO, he would not answer the question. True, though, the answer was not satisfactory but I guess he thinks he can get by with this sort of answers, and so far (for the last 5 years) he managed to do exactly that.
    • CommentAuthorquid
    • CommentTimeFeb 4th 2012
     

    If the situation is as Mark Sapir describes (and I have no reason to doubt it), ie also in private correspondence -- which was explictly offered to OP and the OP being essentially anonymous I take this as a general invitation -- one does not get 'better' information, then in general (that is without having any clue about the particular situation) I consider this as problematic. Still I think the general MO policy is/was by precedent (perhaps this should be changed?) even in less potentially complicated scenarios, to stay away from this type of content. Because what is effectively suggested here is that MO becomes the authorative source for the status of a result in a potentially controversial context. It could no doubt be useful, but it would be quite a step away of what I perceived to be pratise up to know.

    • CommentAuthormarkvs
    • CommentTimeFeb 4th 2012
     
    @quid: I agree with you. That is why I did not start the discussion on MO. But since the question has been asked, it would be improper, I think, to leave it unanswered, because it would create even more rumors and speculation. The most proper way to treat the situation is to ask questions during Joergen's talks. Private correspondence which most often solves the problem does not work in that case, as I said.
  16.  
    Going off on a bit of a tangent, I got hammered really badly in my first year-or-so of being a postdoc, doing research based on a proof by a fine mathematician in a fine journal, which turned out to have an essential gap. It damaged my career tremendously. So the status of these "gaps" or "perceived gaps" is actually tremendously important to our lives and careers; I don't know if MO can contribute to alleviating the problem, but at least it can help show that we are not alone in our confusion about claimed results, details of whose proofs are missing.
  17.  

    I agree with Daniel. I think that if such a gap is found by someone, the author should be notified so as to give him a chance to retract the result or fix the gap. If neither of those is forthcoming, it is a responsibility (unpleasant as it may be) for the error to be made a part of the public record (or corrected).

    There was actually a soft question on exactly this issue many moons ago, and I remember seeing that the most popular answer was something like what I said above.

  18.  

    Looks like it's all sorted out now.

    • CommentAuthormarkvs
    • CommentTimeFeb 6th 2012
     
    @Noah: Right. And the answer basically is: the proof does not exist (is not written up) yet but is expected soon. As you see, the MO question actually helped a lot. I hope there will be more questions like that in the future.

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