Topology, Geometry and Data Seminar - Saugata Basu

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Saugata Basu
May 1, 2018
4:10PM - 5:10PM
Location
Cockins Hall 240

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Add to Calendar 2018-05-01 16:10:00 2018-05-01 17:10:00 Topology, Geometry and Data Seminar - Saugata Basu Title: On the Reeb spaces of definable maps. Speaker: Saugata Basu (Purdue University) Title: We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient. We also show that the Betti numbers of the Reeb space of a map $f$ can be arbitrarily large compared to those of $X$, unlike in the special case of Reeb graphs of manifolds. Nevertheless, in the special case when $f:X \rightarrow Y$ is a semi-algebraic map and $X$ is closed and bounded, we prove a singly exponential upper bound on the Betti numbers of the Reeb space of $f$ in terms of the number and degrees of the polynomials defining $X,Y$ and $f$. (Joint work with Nathanael Cox and Sarah Percival). Seminar URL: https://tgda.osu.edu/activities/tdga-seminar/ Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
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Title: On the Reeb spaces of definable maps.

Speaker: Saugata Basu (Purdue University)

Title: We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient. We also show that the Betti numbers of the Reeb space of a map $f$ can be arbitrarily large compared to those of $X$, unlike in the special case of Reeb graphs of manifolds. Nevertheless, in the special case when $f:X \rightarrow Y$ is a semi-algebraic map and $X$ is closed and bounded, we prove a singly exponential upper bound on the Betti numbers of the Reeb space of $f$ in terms of the number and degrees of the polynomials defining $X,Y$ and $f$.

(Joint work with Nathanael Cox and Sarah Percival).

Seminar URLhttps://tgda.osu.edu/activities/tdga-seminar/

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