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arXiv · 1405.6696

Betti numbers and stability for configuration spaces via factorization homology

Ben Knudsen
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Abstract

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 B\"odigheimer-Cohen-Taylor and F\'elix-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.

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Ben Knudsen. 2014-05-26. Betti numbers and stability for configuration spaces via factorization homology. https://doi.org/10.2140/agt.2017.17.3137

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