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On the connectivity of finite subset spaces

Tom 217 / 2012

Fundamenta Mathematicae 217 (2012), 279-282 MSC: Primary 55P65. DOI: 10.4064/fm217-3-6

Streszczenie

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 $X$.

Autorzy

• Jacob MostovoyDepartamento de Matemáticas
CINVESTAV-IPN
Av. Instituto Politécnico Nacional 2508
Col. San Pedro Zacatenco
México, D.F., C.P. 07360, Mexico
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