Geometric models for classifying spaces of $GLn(Fq)$. - MathOverflow most recent 30 from http://mathoverflow.net2013-05-26T02:44:03Zhttp://mathoverflow.net/feeds/question/33834http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/33834/geometric-models-for-classifying-spaces-of-glnfqGeometric models for classifying spaces of $GLn(Fq)$.Dev Sinha2010-07-29T19:30:22Z2010-07-31T14:18:00Z
<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#34026Answer by Richard Borcherds for Geometric models for classifying spaces of $GLn(Fq)$.Richard Borcherds2010-07-31T14:18:00Z2010-07-31T14:18:00Z<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>