Homotopy equivalences between p-subgroup categories
Algebraic Topology
2014-06-19 v2 Combinatorics
Group Theory
Abstract
Let p be a prime number and G a finite group of order divisible by p. Quillen showed that the Brown poset of nonidentity p-subgroups of G is homotopy equivalent to its subposet of nonidentity elementary abelian subgroups. We show here that a similar statement holds for the fusion category of nonidentity p-subgroups of G. Other categories of p-subgroups of G are also considered.
Keywords
Cite
@article{arxiv.1301.0193,
title = {Homotopy equivalences between p-subgroup categories},
author = {Matthew Gelvin and Jesper Møller},
journal= {arXiv preprint arXiv:1301.0193},
year = {2014}
}
Comments
19 pages. Second version