Homotopical decompositions of simplicial and Vietoris Rips complexes
2021
Online
Elektronische Ressource
Motivated by applications in Topological Data Analysis, we consider decompositionsof a simplicial complex induced by a cover of its vertices. We study how the homotopytype of such decompositions approximates the homotopy of the simplicial complexitself. The difference between the simplicial complex and such an approximationis quantitatively measured by means of the so called obstruction complexes. Ourgeneral machinery is then specialized to clique complexes, Vietoris-Rips complexesand Vietoris-Rips complexes of metric gluings.
QC 20211027
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Homotopical decompositions of simplicial and Vietoris Rips complexes
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Veröffentlichung: | 2021 |
Medientyp: | Elektronische Ressource |
DOI: | 10.1007.s41468-021-00066-2 |
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