Title: Homotopy decompositions at p =2 of sporadic simple groups
Speaker: Professor Stephen D. Smith
Speaker Info: University of Illinois at Chicago
Brief Description:
Special Note:
Abstract:
A survey of parts of the research area of ``subgroup complexes''---which combines techniques from finite group theory, algebraic topology, and combinatorics.Date: Tuesday, October 25, 2005The exposition emphasizes the historical development, from the particular viewpoint of applications to {\em simple} groups and their geometries. The foundations are provided by the work of Tits on buildings, and of Brown and Quillen on simplicial complexes of $p$-subgroups of a group. The discussion continues through some relatively recent theoretical contributions from homotopy theory and from the $p$-local structure of simple groups; these improvements have made possible a joint work of Benson and Smith, which provides for each of the 26 sporadic simple groups a ``small, simplex'' decomposition of its mod 2 group cohomology