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Mathematics > Metric Geometry
Title: Vietoris-Rips Complexes of Split-Decomposable Spaces
(Submitted on 23 Mar 2024)
Abstract: Split-metric decompositions are an important tool in the theory of phylogenetics, particularly because of the link between the tight span and the class of totally decomposable spaces, a generalization of metric trees whose decomposition does not have a ``prime'' component. We use this connection to study the Vietoris-Rips complexes of totally decomposable spaces. In particular, we characterize the homotopy type of the Vietoris-Rips complex of circular decomposable spaces whose metric is monotone. We extend this result to compute the homology of certain non-monotone circular decomposable spaces. We also use the block decomposition of the tight span of a totally decomposable metric to induce a decomposition of the VR complex of a totally decomposable metric.
Submission history
From: Mario Roberto Gómez Flores [view email][v1] Sat, 23 Mar 2024 00:18:03 GMT (353kb,D)
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