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Community: Questions which look like homework, but could be plausible from a reseacher in a distant field.

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    This came up over at Covering maps on Euclidean spaces and spheres. I'd asked Anton what he thought about closing the question, and he decided it would be better to just answer it.

    I'm still undecided about whether this was the right choice. I suspect Anton's thinking is that while this problem could be homework, it could also plausibly come up in the research of a mathematician from a completely different field. There are many problems in many undergraduate courses which I'm sure I'd be unable to answer, but as time passes my research seems more and more likely to have me run into such problems. A good argument for being generous in these situations is that mathoverflow at present is somewhat parochial --- the site has some clearly defined interests, and some significant holes in its coverage of mathematics. One good way to bring a wider range of mathematicians in would be to lend our expertise on these areas! I'm worried that if a numerical analyst runs into an algebraic topology problem they're not familiar with, but happen to know that mathoverflow is full of experts, they'll ask here and be turned away, and we'll lose the chance to have them join the community.

    On the other hand, it sucks to have undergraduate homework problems on mathoverflow!

    What can we do? What should we do?

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    If someone knows what a covering map is, presumably they've seen a textbook definition at some point, or at least know how to find one. Flip a few more pages in the same text and there's the big theorem relating covering spaces to subgroups of the fundamental group.

    If on the other hand the author of the question asked if a submersion $S^n \to S^n$ has to be a diffeomorphism, that indicates the author hasn't been exposed to the covering-space language, and doesn't know the relationship between submersions and fibre bundles. That's the kind of conversation I could expect between research mathematicans that don't know each other's fields very well.

    IMO the bar should be set by how easy it is to find the answer in standard, well-used, well-advertised sources based on the language the author is using. If they're ignorant of major connections, let them know where to find them. If they're asking a question that has an immediate answer on Wikipedia, close the thread and link to the Wikipedia page (at most).
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    I'd also add that context is extremely useful, and that if there isn't any (as there wasn't in that question) then I'd vote to close.

    If I run into something in algebraic geometry that I want to know, then I'd know at the outset that it is unlikely to be something deep and that I wouldn't understand a deep answer. So I'd be careful to explain what I didn't know and what sort of answer I would like. The context would help an algebraic geometer know how much information to give me.

    • CommentAuthorRegenbogen
    • CommentTimeMar 18th 2010
     

    This particular problem was ideally suited for the "Ask a topologist" forum. There such questions are answered extremely fast.

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    Perhaps whoever sees a question like this could ask the original author "could you please provide more motivation by editing your question?"

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