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arXiv · 1109.1952

A spectral sequence for fusion systems

Antonio Díaz Ramos
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Abstract

We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an extension of groups. Nevertheless, the new spectral sequence applies to more general situations like finite simple groups with a strongly closed subgroup and exotic fusion systems with a strongly closed subgroup. We prove an analogue of a result of Stallings in the context of fusion preserving homomorphisms and deduce Tate's p-nilpotency criterion as a corollary.

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Antonio Díaz Ramos. 2013-05-29. A spectral sequence for fusion systems. https://doi.org/10.2140/agt.2014.14.349

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