Subcentric Linking Systems

Abstract

Linking systems are crucial tools for studying the homotopy theory of fusion systems, while also being of profound independent interest from a purely algebraic perspective. However, the classical axioms defining these categories restrict their objects to quasicentric subgroups, which limits the structural flexibility of the theory. To address this limitation, E. Henke [Hen19] proposed expanding the object set to a broader class of subgroups: subcentric subgroups. Utilizing the framework of localities, Henke established that every saturated fusion system admits a unique, up to isomorphism, associated subcentric linking system. In this thesis, we translate Henke’s results into classical categorical language, thereby bypassing the machinery of partial groups and localities. Furthermore, we provide an explicit categorical construction of a subcentric linking system for realizable fusion systems (the fusion systems of finite groups).