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Ultrametrics on Čech homology groups

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Giraldo, A. and Morón, Manuel A. and Sánchez-González, Álvaro (2019) Ultrametrics on Čech homology groups. Topology and its Applications . pp. 1-23. ISSN 0166-8641 (In Press)

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Official URL: https://www.sciencedirect.com/science/article/pii/S0166864119300884#!




Abstract

This paper is devoted to introducing additional structure on Čech homology groups. First, we redefine the Čech homology groups in terms of what we have called approximative homology by using approximative sequences of cycles, just as Borsuk introduced shape groups using approximative maps. From this point on, we are able to construct complete ultrametrics on Čech homology groups. The uniform type (and then the group topology) generated by the ultrametric leads to a shape invariant which we use to deduce topological consequences.


Item Type:Article
Uncontrolled Keywords:Čech homology, Čech homology groups, Approximative cycle and boundary, Approximative homology, Ultrametric
Subjects:Sciences > Mathematics > Group Theory
Sciences > Mathematics > Topology
ID Code:54801
Deposited On:02 Apr 2019 12:24
Last Modified:03 Apr 2019 07:01

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