Geometric models for classifying spaces of \$GLn(Fq)\$. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T02:44:03Z http://mathoverflow.net/feeds/question/33834 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/33834/geometric-models-for-classifying-spaces-of-glnfq Geometric models for classifying spaces of \$GLn(Fq)\$. Dev Sinha 2010-07-29T19:30:22Z 2010-07-31T14:18:00Z <p>The title pretty much says it. In a follow-up to my <a href="http://mathoverflow.net/questions/30113/geometric-model-for-classifying-spaces-of-alternating-groups" rel="nofollow">question about alternating groups</a>, does anyone know of a "geometric" model for \$BGL_n(F_q)\$? By "geometric" I mean "a space you would have heard about even if you aren't studying classifying spaces"; I mean to exclude general constructions such as standard nerve constructions, infinite joins, intractable quotients of frame bundles, etc.</p> http://mathoverflow.net/questions/33834/geometric-models-for-classifying-spaces-of-glnfq/34026#34026 Answer by Richard Borcherds for Geometric models for classifying spaces of \$GLn(Fq)\$. Richard Borcherds 2010-07-31T14:18:00Z 2010-07-31T14:18:00Z <p>Quillens' paper on the Adams conjecture (doi:10.1016/0040-9383(71)90018-8) almost gives an answer. He maps a limit of spaces BGL_n(F_q) to BU and shows that it is not far from an isomorphism. This is related to the plus construction, but cant remember the details offhand. The space BU in turn can be described in terms of Grassmannians. </p>