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arXiv · 1301.0193

Homotopy equivalences between p-subgroup categories

Matthew Gelvin·Jesper Møller
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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.

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Matthew Gelvin, Jesper Møller. 2013-01-02. Homotopy equivalences between p-subgroup categories. https://arxiv.org/abs/1301.0193

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