Extremal Betti numbers of Rips complexes
Michael Goff
TL;DR
This paper establishes upper bounds on the Betti numbers of Vietoris-Rips complexes and provides examples demonstrating complexes with high Betti numbers, advancing understanding of their topological complexity.
Contribution
It introduces new upper bounds for Betti numbers of Rips complexes and supplies explicit examples with high Betti numbers, highlighting their topological richness.
Findings
Upper bounds on Betti numbers are established.
Examples of Rips complexes with high Betti numbers are provided.
The results enhance understanding of the topological complexity of Rips complexes.
Abstract
Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti numbers are given.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics