Eva Belmont: Equivariant homological stability for unordered configuration spaces

Abstract.

In foundational work, McDuff and Segal proved "homological stability" in the setting of unordered configuration spaces \(C_n(M)\) of \(n\) points in an open manifold \(M\); that is, \(H_d(C_n(M)) \cong H_d(C_{n+1}(M))\) for \(n\gg d\). In joint work with J.D. Quigley and Chase Vogeli, we prove an equivariant generalization of McDuff and Segal's result which applies to Bredon homology of unordered configuration spaces on \(G\)-manifolds for a finite abelian group \(G\).