Homology, Homotopy and Applications
Volume 11 (2009)
Remarks on finite subset spaces
Pages: 229 – 250
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 manifold structure. 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 cogroup. Some homological calculations are provided.
finite subsets; connectivity; homology; manifold structure
2010 Mathematics Subject Classification