A spectral sequence for stratified spaces and configuration spaces of points
Algebraic Topology
2017-06-14 v2 Algebraic Geometry
Combinatorics
Geometric Topology
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 \'etale cohomology of algebraic varieties. As an application we prove a very general representation stability theorem for configuration spaces of points.
Keywords
Cite
@article{arxiv.1603.01137,
title = {A spectral sequence for stratified spaces and configuration spaces of points},
author = {Dan Petersen},
journal= {arXiv preprint arXiv:1603.01137},
year = {2017}
}
Comments
23 pages. v2: Several minor improvements and corrections, the arguments in Subsection 3.2 have been fleshed out. Final version, to appear in Geometry & Topology