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2016 Homological stability for families of Coxeter groups
Richard Hepworth
Algebr. Geom. Topol. 16(5): 2779-2811 (2016). DOI: 10.2140/agt.2016.16.2779

Abstract

We prove that certain families of Coxeter groups and inclusions W1W2 satisfy homological stability, meaning that in each degree the homology H(BWn) is eventually independent of n. This gives a uniform treatment of homological stability for the families of Coxeter groups of type A, B and D, recovering existing results in the first two cases, and giving a new result in the third. The key step in our proof is to show that a certain simplicial complex with Wn–action is highly connected. To do this we show that the barycentric subdivision is an instance of the “basic construction”, and then use Davis’s description of the basic construction as an increasing union of chambers to deduce the required connectivity.

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Richard Hepworth. "Homological stability for families of Coxeter groups." Algebr. Geom. Topol. 16 (5) 2779 - 2811, 2016. https://doi.org/10.2140/agt.2016.16.2779

Information

Received: 19 February 2015; Revised: 23 December 2015; Accepted: 12 January 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1383.20022
MathSciNet: MR3572348
Digital Object Identifier: 10.2140/agt.2016.16.2779

Subjects:
Primary: 20F55
Secondary: 20J06

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 5 • 2016
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