Remarks on Finite Subset Spaces

Abstract

This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex $X$ including their connectivity and their top homology groups. It also discusses the inclusion of the singletons into the three fold subset space and shows that this subspace is weakly contractible but generally non-contractible unless $X$ is a co-$H$ group. Some homological calculations are provided.

Several improvements. Sections 5 and 7 expanded out. One missing condition in theorem 1.3 added. Introduction rewritten. To appear in HHA

References in corpus (2)

• Finite subset spaces of closed surfaces
• A hyperbolic approach to exp_3(S^1)