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 $X$.
Keywords:
prove space exp bigvee nonempty subsets cardinality bouquet dimensional spheres k connected shown tuffley implies space exp k connected m connected cell complex
Affiliations des auteurs :
Jacob Mostovoy
1
;
Rustam Sadykov
1
1
Departamento de Matemáticas CINVESTAV-IPN Av. Instituto Politécnico Nacional 2508 Col. San Pedro Zacatenco México, D.F., C.P. 07360, Mexico
@article{10_4064_fm217_3_6,
author = {Jacob Mostovoy and Rustam Sadykov},
title = {On the connectivity of finite subset spaces},
journal = {Fundamenta Mathematicae},
pages = {279--282},
year = {2012},
volume = {217},
number = {3},
doi = {10.4064/fm217-3-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm217-3-6/}
}
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AU - Rustam Sadykov
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Jacob Mostovoy; Rustam Sadykov. On the connectivity of finite subset spaces. Fundamenta Mathematicae, Tome 217 (2012) no. 3, pp. 279-282. doi: 10.4064/fm217-3-6
