Extremal Betti Numbers of Rips Complexes
نویسنده
چکیده
Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti
منابع مشابه
Random Geometric Complexes
We study the expected topological properties of Čech and Vietoris-Rips complexes built on randomly sampled points in R. These are, in some cases, analogues of known results for connectivity and component counts for random geometric graphs. However, an important difference in this setting is that homology is not monotone in the underlying parameter. In the sparse range, we compute the expectatio...
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