A spectral sequence for stratified spaces and configuration spaces of points

Petersen, Dan¹

¹ Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

Geometry & topology, Tome 21 (2017) no. 4, pp. 2527-2555.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.2527

Classification : 55R80, 55T05, 32S60, 14F25, 55N30
Keywords: configuration spaces, representation stability, homological stability, stratified spaces, spectral sequence

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