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.
"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