once bitten, twice shy (updated)
(Having found arXiv moderators’ actions a bit odd in the past, I’m not going to stress unduly about why this is being accepted as a new submission as opposed to a replacement of an existing one.)
I don’t see any acknowledgment in either paper of the error in 0906.0107, but perhaps I’ve not looked hard enough. Certainly, after my previous abortive attempt, I have no real appetite for reading the new version, since the calculations appear to be equally opaque (in terms of motivation) and equally illegibly typeset. As with the previous version, I can’t see any attempt to give a conceptual framework for the supposed proof, nor to provide context in terms of previous work of the author and others.
So: no thanks, this time. I think I’ll wait (with some interest, if not with bated breath) for the experts to finish picking over this one.
Update 3rd Feb 2011: J. T. Moore has just posted a note on the arXiv
1102.0747 A note on Shavgulidze’s papers concerning the amenability problem for Thompson’s group $F$
with some discussion of both preprints mentioned in this post, and some of the work done by various people examining Shavgulidze’s purported proof.