Subject: [AlgTopList] Re: Cohomology of infinite symmetric group Date: Sat, 15 Dec 2001 08:05:46 -0500 From: "Vidhyanath Rao" To: "Kevin Walker" CC: [from sci.math.research] > A physicist friend of mine is very anxious to know what > H^4(S_\infinity) is. (By S_\infinity I mean the group of > permutations of the natural numbers with finite support.) > ... He conjectures that the > image of the Pontryagin class > (induced from the inclusion of S_\infinity into the > orthogonal group via permutation matrices) is non-zero in > H^4(S_\infinity). The (co)homology of the infinite symmetric group (defined as the union of all symmetric groups via the natural inclusions, I think the same as your S_\infty) is known (at least mod all primes). So the conjecture must be settlable. I am copying this message to the alg top mailing list which should produce faster answer than me looking up the references. [It should fall out of BSigma_\infty -> BO -> QS^1, I think]. Regards Nath Rao