User fred - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T01:51:16Z http://mathoverflow.net/feeds/user/23185 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95088/computation-of-stable-cohomology-ring-of-sl-nz-using-algebraic-topology Computation of stable cohomology ring of SL_n(Z) using algebraic topology Fred 2012-04-24T22:54:26Z 2012-04-24T22:54:26Z <p>It is known that $H^k(SL(n,\mathbb{Z}))$ is independent of $n$ for $n \gg k$, so we can define a stable cohomology ring $$V = \text{lim}_{n \rightarrow \infty} H^{\ast}(SL(n,\mathbb{Z});\mathbb{R}).$$ Using analytic tools, Borel proved that $V$ is an exterior algebra generated in degrees $3, 5, 7, \ldots$. Is there proof of this using more traditional algebraic topology tools?</p> http://mathoverflow.net/questions/95477/tangled-knot-function/95481#95481 Comment by Fred Fred 2012-04-29T04:20:28Z 2012-04-29T04:20:28Z Here's a nice recent paper of Birman and Kofman on the subject that also has a good bibliography of previous work : <a href="http://www.math.columbia.edu/~jb/bk-lorenz-jtop.pdf" rel="nofollow">math.columbia.edu/~jb/bk-lorenz-jtop.pdf</a>