English

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 XX 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 XX is a co-HH 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

R2 v1 2026-06-21T12:14:11.563Z