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What's the status of this claimed proof?

• Louis F. McAuley, A Proof of the Hilbert-Smith Conjecture, 2001, arXiv:math/0103215.

John Baez (talk) 15:09, 16 July 2025 (UTC)[reply]

Have you tried asking on Mathoverflow? (I was not aware of this preprint but i'm far from a specialist on this topic ; the fact that there is a flurry of postings to the arxiv seems to indicate that the paper was read and objected to at the time so hopefully somebody remembers it). jraimbau (talk) 14:31, 17 July 2025 (UTC)[reply]

I was going to ask the question myself but i found that somebody else did so 15 years ago (before McAuley passed) and as could be expected the preprint was found to be incorrect some time after its appearance (though the answer is not very detailed). Let me quote from the answer by Igor Belegradek:

I am no expert in the subject, but I have heard that McAuley's preprint "A Proof of the Hilbert-Smith Conjecture" is incorrect. A while ago there was a conference in Istanbul, where McAuley worked at the time. The conference was devoted to studying this preprint, and in particular, Shepin, who earlier proved with Repov the HS-conjecture for Lipschitz actions, was there. If memory serves me, Shepin found that McAuley's argument actually proves something stronger to which there was a counterexample known.

(The question is : https://mathoverflow.net/questions/32656/status-of-hilbert-smith-conjecture-and-h-s-conjecture-for-h%c3%b6lder-actions.)jraimbau (talk) 12:49, 23 July 2025 (UTC)[reply]