User karl - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T03:00:49Z http://mathoverflow.net/feeds/user/8186 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/34645/euler-characteristic-of-general-linear-group Euler Characteristic of General Linear Group Karl 2010-08-05T15:55:44Z 2012-04-10T12:31:36Z <p>(Edited) How can I find Euler-Poincare Index with compact support of General Linear Group over $\mathbb{R}$. For example let $A$ be a locally closed subset of a manifold $X$ then: $\chi_c(A)=\chi(R\Gamma(X;\mathbb{R}_A))=\chi(R\Gamma_c(A;\mathbb{R}_A))$</p> <p>Which, in a smooth case it is the same as alternating sum of Betti numbers of de Rham cohomologies with compact support. Thank you.</p> http://mathoverflow.net/questions/34645/euler-characteristic-of-general-linear-group/34761#34761 Comment by Karl Karl 2010-08-07T10:33:09Z 2010-08-07T10:33:09Z Thank you all. My idea was to use Poincare Duality for $n&gt;1$. Then using a homotopy equivalence of $GL(n)$ and $SL(n)$. Now, since Euler characteristic of a compact Lie group $Sl(n)$ for $n&gt;1$ is zero. We will have $chi_c(Gl(n))=0.$ Which coincides with above answers.