Mapping class group and property (T) Does anyone know what the current expert consensus is concerning the status of the question as to whether the mapping class group of a surface has property (T)?
There is a short (21 page) paper by J. Andersen which purports to use quantum representations to prove that it does not.  See here.  It was released in 2007, but it does not seem to have yet been accepted by a journal.  I have asked several experts (on the mapping class group and on property (T)), and none of them seem to understand the details of this paper.  One or two of them alluded to issues they had heard might exist, but they were pretty vague as to what these issues might be.
 A: Dear Michael,
There certainly is a complete proof of this result including a proof of theorem 5. Theorem 5
follows essentially from my joint work with Kenji Ueno presented in a series of 4 joint papers. These papers are all on the archive and three of them has been published/accepted for publication and the four is submitted for publication. I am currently writing up the paper [A6] "Mapping class group invariant unitarity of the Hitchin connection over Teichmuller space", where a detailed argument for Theorem 5 will be given. It is Corollary 1 of that paper. As soon as that paper is finished I will put it on the archive and I will submit that paper together with my paper
"The mapping class group does not have Property T" for publication.
I am not aware of any problems with my proof.- I have ever only received one email suggesting there was a problem (from Mark Sapir), which claimed that Vaughan Jones knew of a problem with the paper. I immediately wrote to Vaughan to ask him what this problem was and he applied right away he didn't know of any mistakes in my argument. Mark right after acknowledged via email that he had misunderstood Vaughan.
I am more than happy to answer all questions via email regarding this result and its proof, so Michael, if you would please let me know who you are and your email address, I will get in touch right away.
Yours,
Jørgen Ellegaard Andersen
Note added by Ian Agol: Andersen's paper proving Theorem 5 appeared on the Arxiv recently.
