The integral cohomology algebras of ordered configuration spaces of spheres
type: Item
instance of: scholarly article
title: The integral cohomology algebras of ordered configuration spaces of spheres
zbMATH Open document ID: 0992.55014
author: Eva-Maria Feichtner
author: Günter M. Ziegler
published in: Documenta Mathematica
publication date: 2000-04-16T00:00:00Z
full work available at URL: https://eudml.org/doc/49352
full work available at URL: 05.html
review text: Summary: We compute the cohomology algebras of spaces of ordered point configurations on spheres, \(F(S^k,n)\), with integer coefficients. For \(k=2\) we describe a product structure that splits \(F(S^2,n)\) into well-studied spaces. For \(k>2\) we analyze the spectral sequence associated to a classical fiber map on the configuration space. In both cases we obtain a complete and explicit description of the integer cohomology algebra of \(F(S^k,n)\) in terms of generators, relations and linear bases. There is \(2\)-torsion occuring if and only if \(k\) is even. We explain this phenomenon by relating it to the Euler classes of spheres. Our rather classical methods uncover combinatorial structures at the core of the problem.
Mathematics Subject Classification ID: 55R80
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 55R20
zbMATH DE Number: 1431775
zbMATH Keywords: subspace arrangement
zbMATH Keywords: integral cohomology algebras
zbMATH Keywords: fibration
zbMATH Keywords: Serre spectral sequence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1431775