On thick diagonals and their complements
type: Item
instance of: scholarly article
title: On thick diagonals and their complements
zbMATH Open document ID: 1329.55020
author: Faten Labassi
published in: Journal of Homotopy and Related Structures
publication date: 2015-09-21T00:00:00Z
review text: The author studies configuration spaces. More precisely, let \(X\) be a connected CW-complex, denote by \(D_{d}(X,n)\) the subspace of \(n\)-tuples, \((x_{1},\ldots,x_{n})\), \(x_{i}\in X\), having \(d\) coordinates which coincide and set \(F^{d+1}(X,n)=X^n\backslash D_{d}(X,n)\). In the case \(n<2d\), the author proves the existence of a splitting of the suspension, \(\Sigma D_{d}(X,n)\), in a wedge of smash products of \(X\). The example of \(D_{2}(S^m,4)\) shows the necessity of the restriction \(n<2k\). The author determines also the Euler characteristic and the cohomology ring of \(F^{n-1}(X,n)\) when \(X\) is an orientable closed manifold.
reviewed by: Daniel Tanré
Mathematics Subject Classification ID: 55R80
Mathematics Subject Classification ID: 55P15
zbMATH DE Number: 6483842
zbMATH Keywords: configuration spaces
zbMATH Keywords: stable splitting
zbMATH Keywords: Cohomology ring
MaRDI profile type: Publication
full work available at URL: s40062-013-0065-0
OpenAlex ID: W2036878022
cites work: Topology of configuration space of two particles on a graph. I.
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DOI: 10.1007/S40062-013-0065-0
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description: scientific article; zbMATH DE number 6483842