Abstract
Topological persistence is, by now, an established paradigm for constructing robust topological invariants from point cloud data: the data are converted into a filtered simplicial complex, the complex gives rise to a persistence module, and the module is described by a persistence diagram. In this paper, we study the geometry of the spaces of persistence modules and diagrams, with special attention to Cech and Rips complexes. The metric structures are determined in terms of interleaving maps between modules and matchings between diagrams. We show that the relationship between the Cech and Rips complexes is governed by certain `coherence' conditions on the corresponding families of interleavings or matchings.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
