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Two years ago, Joel Friedman submitted a paper purporting to prove the Hanna Neumann Conjecture, which eventually turned out to contain a fatal bug and was withdrawn. Quite recently, Friedman repeated his attempt at proof with paper "Sheaves on Graphs and a Proof of the Hanna Neumann Conjecture": http://arxiv.org/abs/1105.0129 . Has this attempt been verified by anyone or is still under review?

Marcin Kotowski
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    Is MO the right place for this kind of discussion? – Alain Valette Jun 03 '11 at 15:30
  • Regarding the comment, I have no particular personal opinion, but the question below to me seems quite comparable: http://mathoverflow.net/questions/26821/is-thompsons-group-f-amenable –  Jun 03 '11 at 15:46
  • And also similar to this: http://mathoverflow.net/questions/66759/collatz-conjecture-solved-closed – Gerald Edgar Jun 03 '11 at 17:07
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    I don't think it is appropriate to discuss such things here, and I believe there was a meta discussion to that effect when people started posting questions about Deolalikar's paper. – Qiaochu Yuan Jun 03 '11 at 17:44
  • I agree with Qiaochu. The Thompson's group situation was a bit exceptional because there had been a lot of discussion of it online, and the question was asking for a summary of that discussion. In general I think it's bad for MO to be taking positions on peoples preprints, as we don't want MO making enemies. – Noah Snyder Jun 03 '11 at 17:50
  • Let me just say very briefly why I think that this question is much closer to the one I linked to (which stayed open, without discussion, at least there is no obvious sign of discussion on the question) than to the other ones mentioned. a. It concerns a well-known but not 'classically famous' problem (say, RH, PvsNP, maybe Collatz, Golbach,..). b. There seems to be some back-and-forth regarding the specific contribution (as opposed to the general problem). –  Jun 03 '11 at 17:54
  • Noah Snyder, sorry I did not see your comment before writing my second one. Also this will be my last comment on this as I actually said I have no opinion, which is the case; I only defend my analogy argument (but needless to say one does not have to follow every single, possibly 'bad', precedent). Didn't the Thompson question precisely ask for taking positions as the other online discussion was inconclusive for the questioner? –  Jun 03 '11 at 18:08
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    My motivation for asking this question is: a) this is not a "high profile" problem as RH, Collatz or P/NP, so unlikely to attract much attention on blogs etc. (= hard to know, for me, what the community thinks of it), b) the technology used in the proof seems quite nonstandard, maybe someone knowledgeable could e.g. put this in wider context, previous proof attempts, whether this has any heuristic chance of succeeding etc – Marcin Kotowski Jun 03 '11 at 18:45
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    Meta thread - http://tea.mathoverflow.net/discussion/1059/discussing-preprints-on-mo/ – François G. Dorais Jun 03 '11 at 20:23
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    For those who is interested in the Hannah Neumann conjecture, both Friedman and Mineyev are going to participate in a Banff workshop http://www.birs.ca/events/2011/5-day-workshops/11w5141 in June, and Mineyev is going to participate in the AIM workshop http://www.aimath.org/ARCC/workshops/l2invfggroups.html in September. I am co-organizing the AIM workshop and Miklos Abert is co-organizing both. So if not by the end of June, then by the end of September, we will know at least if Mineyev's (shorter) proof is correct. –  Jun 06 '11 at 05:50
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    Mineyev's proof has been verified. It is of course an amazing thing that one can give a 2-page proof of a 40-year old problem. –  Sep 16 '11 at 05:01
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    Friedman's paper has been accepted to Memoirs http://www.ams.org/cgi-bin/mstrack/accepted_papers/memo and also has a simplification by Dicks. – Benjamin Steinberg May 01 '13 at 14:11

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I don't think that this latest round has been independently verified.

Igor Mineyev has also announced a solution. See http://www.math.uiuc.edu/~mineyev/math/

Autumn Kent
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