turkmath.org

A fusion system F on a finite p-group S is a category whose objects are the subgroups of S, and whose morphisms are injective group homomorphisms satisfying certain axioms. For a discrete group G with a Sylow p-subgroup S, the fusion system F_S(G) is defined by taking morphisms as conjugation maps induced by elements in G. We see fusion systems in finite group theory, in modular representation theory, and in topology while studying p-completed classifying spaces. In this talk, I will explain some of the places where we see fusion systems in topology. I will also mention some results from our recent work with Muhammed Said Gündoğan.