A fusion system over a p-group S is a category whose objects form the set of all subgroups
of S, whose morphisms are certain injective group homomorphisms, and which satisfies …

We define and characterize a class of $ p $-complete spaces $ X $ which have many of the
same properties as the $ p $-completions of classifying spaces of finite groups. For example …

A p-local nite group consists of a nite p-group S, together with a pair of categories ðF; LÞ, of
which F is modeled on the conjugacy (or fusion) in a Sylow subgroup of a nite group. The …

Let C be a small category and R a commutative ring with a 1. A representation of C over R is
a functor F: C→ R-mod where R-mod is the category of R-modules. This general concept …

We study homotopy equivalences of p-completions of classifying spaces of finite groups. To
each finite group G and each prime p, we associate a finite category ℒ pc (G) with the …

This book is intended as an overview of a research area that combines geometries for
groups (such as Tits buildings and generalizations), topological aspects of simplicial …

A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-
local analog of a compact Lie group. It has long been the hope, and later the conjecture, that …

We present a version of a proof by Andy Chermak of the existence and uniqueness of centric
linking systems associated with arbitrary saturated fusion systems. This proof differs from the …

Abstract We prove the Martino–Priddy conjecture for an odd prime p: the p-completions of
the classifying spaces of two groups G and G are homotopy equivalent if and only if there is …

Classifying endotrivial $ kG $-modules, ie, elements of the Picard group of the stable module
category for an arbitrary finite group $ G $, has been a long-running quest. By deep work of …