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The homotopy theory of fusion systems

By Carles Broto, Ran Levi and Bob Oliver


The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p-completed classifying spaces of finite groups. These spaces occur as the “classifying spaces ” of certain algebraic objects, which we call p-local finite groups. A p-local finite group consists, roughly speaking, of a finite p-group S and fusion data on subgroups of S, encoded in a way explained below. Our starting point is our earlier paper [BLO] on p-completed classifying spaces of finite groups, together with the axiomatic treatment by Lluís Puig [Pu], [Pu2] of systems of fusion among subgroups of a given p-group. The p-completion of a space X is a space X ∧ p which isolates the properties of X at the prime p, and more precisely the properties which determine its mod p cohomology. For example, a map of spaces X f −− → Y induces a homotopy equivalenc

Year: 2013
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