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A
spectral sequence for stratified spaces and configuration
spaces of points
Dan Petersen |
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Geometry & Topology 21 (2017) 2527–2555
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Correction: 10.2140/gt.2021.25.2699
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 55R80
Secondary: 55T05, 32S60, 14F25, 55N30
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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
Correction: 3 September 2021
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Authors |
| Dan Petersen | |
| Department of Mathematical
Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark |
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