Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 1 (2014), 349-378.
A spectral sequence for fusion systems
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 –nilpotency criterion as a corollary.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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