Remarks on Finite Subset Spaces

Details Remarks on Finite Subset Spaces Remarks on Finite Subset Spaces

2009-02-22

arxiv.org/abs/0902.3773v2

Mathematics

Algebraic Topology

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

Scientific paper

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.

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