Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

Remarks on finite subset spaces

Pages: 229 – 250

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n2.a12


Sadok Kallel (Laboratoire Painlevé, Université des Sciences et Technologies de Lille, France)

Denis Sjerve (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)


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

55S15, 55U10

Published 1 January 2009