Dahisy Lima

Wednesday, November 11th, 2020. Gmeet at 4:20 pm

**Title: On the Interplay between Topology and Dynamics on Singular Surfaces**

**Abstract**: In Morse Theory, the central idea is to study the relationship between the

topology of a differentiable manifold and the structure of critical points of a realvalued differentiable function defined on it (in other words, the gradient flow

associated to this function).

In this talk, we make use of Conley Index Theory to describe the change in the

topology of the level set of a singular surface as one passes through a GS

singularity (cone, cross-cap, double crossing and triple crossing singularities). We

use of Handle Theory and Reeb graphs in order to keep track of the changes in the

connectivity of the level sets