Topology, Geometry and Data Seminar - Osman Okutan

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Osman Berat Okutan
February 12, 2019
4:10PM - 5:10PM
Location
Cockins Hall 240

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Add to Calendar 2019-02-12 16:10:00 2019-02-12 17:10:00 Topology, Geometry and Data Seminar - Osman Okutan Title: The distortion of the Reeb quotient Map Speaker: Osman Berat Okutan (Ohio State University) Abstract: Given a metric space $X$ and a function $f:X \rightarrow \mathbb{R}$, the Reeb construction gives metric a space $Xf$ together with a quotient map $X \rightarrow Xf$. Under suitable conditions $Xf$ becomes a metric graph and can therefore be used as a graph approximation to $X$. The Gromov-Hausdorff distance from $Xf$ to $X$ is bounded by the half of the metric distortion of the quotient map. In this paper we consider the case where $X$ is a compact Riemannian manifold and $f$ is an excellent Morse function. In this case we provide bounds on the distortion of the quotient map which involve the first Betti number of the original space and a novel invariant which we call thickness. Seminar URL: https://tgda.osu.edu/ Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
Description

Title: The distortion of the Reeb quotient Map

SpeakerOsman Berat Okutan (Ohio State University)

Abstract: Given a metric space $X$ and a function $f:X \rightarrow \mathbb{R}$, the Reeb construction gives metric a space $Xf$ together with a quotient map $X \rightarrow Xf$. Under suitable conditions $Xf$ becomes a metric graph and can therefore be used as a graph approximation to $X$. The Gromov-Hausdorff distance from $Xf$ to $X$ is bounded by the half of the metric distortion of the quotient map. In this paper we consider the case where $X$ is a compact Riemannian manifold and $f$ is an excellent Morse function. In this case we provide bounds on the distortion of the quotient map which involve the first Betti number of the original space and a novel invariant which we call thickness.

Seminar URLhttps://tgda.osu.edu/

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