Geodesic
Twisted homological stability for configuration spaces
Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 145-178.

Voir la notice de l'article provenant de la source International Press of Boston

Let $M$ be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence $\lbrace C_n (M) \rbrace$ of configuration spaces of $n$ unordered, distinct points in $M$ is homologically stable with coefficients in $\mathbb{Z}$ — in each degree, the integral homology is eventually independent of $n$. The purpose of this paper is to prove that this phenomenon also holds for homology with twisted coefficients. We first define an appropriate notion of finite-degree twisted coefficient system for $\lbrace C_n (M) \rbrace$ and then use a spectral sequence argument to deduce the result from the untwisted homological stability result of McDuff and Segal. The result and the methods are generalisations of those of Betley for the symmetric groups.
DOI : 10.4310/HHA.2018.v20.n2.a8
Classification : 55R80, 57N65
Keywords: configuration space, homological stability, polynomial twisted coefficients 
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     author = {Martin Palmer},
     title = {Twisted homological stability for configuration spaces},
     journal = {Homology, homotopy, and applications},
     pages = {145--178},
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     number = {2},
     year = {2018},
     doi = {10.4310/HHA.2018.v20.n2.a8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a8/}
}
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Martin Palmer. Twisted homological stability for configuration spaces. Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 145-178. doi : 10.4310/HHA.2018.v20.n2.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a8/

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