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Cellular approximations of fusion systems

Guille Carrión, Natàlia Castellana, Alberto Gavira-Romero

Abstract

In this paper we study the cellularization of classifying spaces of saturated fusion systems with respect to classifying spaces of finite p-groups. We give explicit algebraic criteria to decide when a classifying space is cellular. Moreover, we describe computations for a given family of exotic examples introduced by Díaz-Ruiz-Viruel.

Cellular approximations of fusion systems

Abstract

In this paper we study the cellularization of classifying spaces of saturated fusion systems with respect to classifying spaces of finite p-groups. We give explicit algebraic criteria to decide when a classifying space is cellular. Moreover, we describe computations for a given family of exotic examples introduced by Díaz-Ruiz-Viruel.

Paper Structure

This paper contains 5 sections, 26 theorems, 44 equations.

Table of Contents

  1. The homotopy theory of fusion systems
  2. Homotopy properties of cellular spaces
  3. The kernel of a map from a classifying space
  4. Cellular properties of the classifying space of a saturated fusion system
  5. The cellularization of the classifying spaces of a family of exotic fusion systems

Key Result

Theorem 1.6

Let $(S,\mathcal{F})$ be a saturated fusion system. Up to equivalence, there exists a unique centric linking system $\mathcal{L}$ associated to $\mathcal{F}$.

Theorems & Definitions (71)

  • Definition 1.1
  • Example 1.2
  • Example 1.4
  • Definition 1.5
  • Theorem 1.6: MR3118305Oliver-ExistenceL
  • Definition 1.7
  • Proposition 1.8
  • proof
  • Theorem 1.10: MR2302515
  • Definition 1.11
  • ...and 61 more