Remarks on Finite Subset Spaces
Algebraic Topology
2009-08-03 v2
Abstract
This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex 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 is a co- group. Some homological calculations are provided.
Keywords
Cite
@article{arxiv.0902.3773,
title = {Remarks on Finite Subset Spaces},
author = {Sadok Kallel and Denis Sjerve},
journal= {arXiv preprint arXiv:0902.3773},
year = {2009}
}
Comments
Several improvements. Sections 5 and 7 expanded out. One missing condition in theorem 1.3 added. Introduction rewritten. To appear in HHA