Topology, Geometry and Data Seminar - Saugata Basu

April 27, 2018
Tuesday, May 1, 2018 - 4:10pm to 5:10pm
Cockins Hall 240
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 URLhttps://tgda.osu.edu/activities/tdga-seminar/

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