On the connectivity of finite subset spaces
Volume 217 / 2012
Fundamenta Mathematicae 217 (2012), 279-282
MSC: Primary 55P65.
DOI: 10.4064/fm217-3-6
Abstract
We prove that the space $\exp_k \bigvee S^{m+1}$ of nonempty subsets of cardinality at most $k$ in a bouquet of $m+1$-dimensional spheres is $(m+k-2)$-connected. This, as shown by Tuffley, implies that the space $\exp_k X$ is $(m+k-2)$-connected for any $m$-connected cell complex $X$.
