On the Interplay between Topology and Dynamics on Singular Surfaces
Date(s) : 23/05/2024 iCal
11h00 - 12h00
In this talk, we address the advances in the study of Gutierrez-Sotomayor singular flow (GS flow, for short) on closed singular 2-manifolds. We make use of the 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). Moreover, we explore the dynamical behaviour of GS-singularities within GS-flows through homotopical perturbations to achieve a « minimal flow » into the class of homotopy equivalent spaces. This is done by describing the qualitative aspects of the flow in terms of a chain complex generated by the singularities of the flow and establishing a homotopical cancellation theory of GS-singularities.
Emplacement
I2M Saint-Charles - Salle de séminaire
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