TL;DR
This paper computes the rational homology of finite subset spaces of spheres, providing a complete description and partial results for integral homology in specific degrees.
Contribution
It offers the first complete rational homology calculation for finite subset spaces of spheres and partial integral homology results.
Findings
Complete rational homology for finite subset spaces of spheres
Integral homology in top degrees determined
Partial integral homology in codimension d obtained
Abstract
We find the complete rational homology for the finite subset spaces of a -dimensional sphere. We also determine the integral homology in top degrees and obtain a partial description of it in codimension .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Geometric and Algebraic Topology