## Algebraic & Geometric Topology

### A spectral sequence for fusion systems

Antonio Díaz Ramos

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 349-378.

Dates
Received: 13 December 2012
Revised: 22 May 2013
Accepted: 29 May 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715804

Digital Object Identifier
doi:10.2140/agt.2014.14.349

Mathematical Reviews number (MathSciNet)
MR3158762

Zentralblatt MATH identifier
1297.55019

#### Citation

Díaz Ramos, Antonio. A spectral sequence for fusion systems. Algebr. Geom. Topol. 14 (2014), no. 1, 349--378. doi:10.2140/agt.2014.14.349. https://projecteuclid.org/euclid.agt/1513715804

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