Algebraic & Geometric Topology

A spectral sequence for fusion systems

Antonio Díaz Ramos

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55T10: Serre spectral sequences
Secondary: 55R35: Classifying spaces of groups and $H$-spaces 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

Lyndon–Hochschild–Serre spectral sequence fusion system strongly closed subgroup Tate's nilpotency criterion


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.

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