Geodesic
Betti numbers and stability for configuration spaces via factorization homology
Knudsen, Ben1
1 Department of Mathematics, Harvard University, Cambridge, MA, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 3137-3187

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold M, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology of M. By locating the homology of each configuration space within the Chevalley–Eilenberg complex of this Lie algebra, we extend theorems of Bödigheimer, Cohen and Taylor and of Félix and Thomas, and give a new, combinatorial proof of the homological stability results of Church and Randal-Williams. Our method lends itself to explicit calculations, examples of which we include.

DOI : 10.2140/agt.2017.17.3137
Classification : 57R19, 17B56, 55R80
Keywords: configuration spaces, factorization homology, Lie algebras, homological stability

Knudsen, Ben 1

1 Department of Mathematics, Harvard University, Cambridge, MA, United States 
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Knudsen, Ben. Betti numbers and stability for configuration spaces via factorization homology. Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 3137-3187. doi: 10.2140/agt.2017.17.3137

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