Homological stability of oriented configuration spaces
type: Item
instance of: scholarly article
title: Homological stability of oriented configuration spaces
zbMATH Open document ID: 0891.55013
author: Martin A. Guest
author: Kohhei Yamaguchi
author: Andrzej Kozłowski
published in: Journal of Mathematics of Kyoto University
publication date: 1998-07-19T00:00:00Z
review text: Let \(F(X,d)\) be the ordered configuration space \(\{(x_1, \dots, x_d)\in X^d: x_i \neq x_j\) if \(i\neq j\}\) and let \(C_d(X)\) denote the quotient space \(F(X,d)/\Sigma_d\), where \(\Sigma_d\) is the symmetric group of \(d\) letters \(\{1,2, \dots,d\}\) and it acts by the permutation of coordinates. The space is called the unordered configuration space of \(d\) distinct points in \(X\) and there are many interesting applications in homotopy theory. For the alternation subgroup \(A_d\subset \Sigma_d\) of index 2, let \(\widetilde C_d(X)\) be the quotient space \(F(X,d)/ A_d\) and it is also called the oriented configuration space of \(d\) distinct points in \(X\). In this paper, the authors study the homological stability of the stabilization map \(\widetilde C_d (X)\to \widetilde C_{d+1} (X)\) for the case \(X=M_g-\)\{finite points\} using several results concerning the homologies of configuration spaces due to Bödigheimer, F. Cohen and L. Taylor. This result may be useful for studying the recent stability phenomena of several moduli spaces.
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 1062467
zbMATH Keywords: moduli space
zbMATH Keywords: configuration space
zbMATH Keywords: stabilization map
reviewed by: Mamoru Mimura
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518453
OpenAlex ID: W1509016220
DOI: 10.1215/KJM/1250518453
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description: scientific article; zbMATH DE number 1062467