Large-scale geometry of the Rips filtration
The seminar series covers topics in Algebra and Topology
Date & time
Date/time
4 Sep 2024 3:00pm - 4 Sep 2024 4:00pm
Speaker
Speakers
Robert Tang (Xi’an Jiaotong-Liverpool University)
Event series
Event series
Contact
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Description
Abstract:
Given a metric space $X$ and a scale parameter $\sigma \geq 0$, the Rips graph $Rips^\sigma X$ has $X$ as its vertex set, with two vertices declared adjacent whenever their distance is at most $\sigma$. A classical fact is that $X$ is a quasigeodesic space precisely if it is quasi-isometric to its Rips graph at sufficiently large scale.
By considering all possible scales, we obtain a directed system of graphs known as the Rips filtration. How does the large-scale geometry of $Rips^\sigma X$ evolve as $\sigma \to \infty$? Is there a meaningful notion of limit? It turns out that the answers depends on whether we work up to quasi-isometry or coarse equivalence. In this talk, I will discuss some results inspired by these questions.
Location
Rm 1.33, Hanna Neumann Building #145
-35.275389387895, 149.11926090717