Homology, Homotopy and Applications

Remarks on finite subset spaces

Sadok Kallel and Denis Sjerve

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Abstract

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.

Article information

Source
Homology Homotopy Appl., Volume 11, Number 2 (2009), 229-250.

Dates
First available in Project Euclid: 27 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296138520

Mathematical Reviews number (MathSciNet)
MR2591920

Zentralblatt MATH identifier
1186.55010

Subjects
Primary: 55U10: Simplicial sets and complexes 55S15: Symmetric products, cyclic products

Keywords
Finite subsets connectivity homology manifold structure

Citation

Kallel, Sadok; Sjerve, Denis. Remarks on finite subset spaces. Homology Homotopy Appl. 11 (2009), no. 2, 229--250. https://projecteuclid.org/euclid.hha/1296138520


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