Cellular approximations of fusion systems

TL;DR

This paper investigates the cellularization of classifying spaces of saturated fusion systems relative to finite p-groups, providing algebraic criteria and explicit computations for exotic examples.

Contribution

It introduces algebraic criteria for cellularity of classifying spaces and performs explicit calculations for specific exotic fusion systems.

Findings

Algebraic criteria for cellularity of classifying spaces.

Explicit computations for exotic fusion systems.

Criteria applicable to a broad class 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 D\'iaz-Ruiz-Viruel.