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