Higher limits over the fusion orbit category

Abstract: One of the open problems related to the homotopy theory of fusion systems asks whether or not the subgroup decomposition for a p-local finite group is sharp. The sharpness of the subgroup decomposition is known to be true for finite group fusion systems, but in general this problem is still open except for some special cases. I will describe some new methods for calculating higher limits over the fusion orbit category of a discrete group and show how these new methods can be applied to the sharpness problem. In particular, we show that the subgroup decomposition for p-local finite groups is sharp, if it is sharp for every p-local finite group with nontrivial center.

algebraic topologycategory theorygroup theoryK-theory and homology

Audience: researchers in the topic

Cihan Okay

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