Abstract
Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold , possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology of . 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.
Citation
Ben Knudsen. "Betti numbers and stability for configuration spaces via factorization homology." Algebr. Geom. Topol. 17 (5) 3137 - 3187, 2017. https://doi.org/10.2140/agt.2017.17.3137
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