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Abstract
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We prove that certain families of Coxeter groups and inclusions
satisfy homological stability, meaning that in each degree the homology
is eventually
independent of
.
This gives a uniform treatment of homological stability for the families of Coxeter groups
of type
,
and
,
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
–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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Keywords
homological stability, Coxeter groups
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Mathematical Subject Classification 2010
Primary: 20F55
Secondary: 20J06
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Publication
Received: 19 February 2015
Revised: 23 December 2015
Accepted: 12 January 2016
Published: 7 November 2016
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