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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A spectral sequence for stratified spaces and configuration spaces of points

Dan Petersen

Geometry & Topology 21 (2017) 2527–2555
Abstract

We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported cohomology groups of closed strata and the reduced cohomology groups of the poset of strata. Several familiar spectral sequences arise as special cases. The construction is sheaf-theoretic and works both for topological spaces and for the étale cohomology of algebraic varieties. As an application we prove a very general representation stability theorem for configuration spaces of points.

Keywords
configuration spaces, representation stability, homological stability, stratified spaces, spectral sequence
Mathematical Subject Classification 2010
Primary: 55R80
Secondary: 55T05, 32S60, 14F25, 55N30
References
Publication
Received: 17 May 2016
Revised: 14 July 2016
Accepted: 29 August 2016
Published: 19 May 2017
Proposed: Benson Farb
Seconded: Ralph Cohen, Dan Abramovich
Authors
Dan Petersen
Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
DK-2100 Copenhagen
Denmark