Seminar Announcement
Date: Wednesday, 22 January 2025
Time: 3:30 PM
Venue: Seminar Hall
Doing Morse theory without Smale condition
Ipsita Datta
ETH Zuerich.
22-01-25

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Abstract

We will present Morse homology in the classical way and also using Fredholm sections of an appropriate bundle. We will point out how the Smale condition allows us to define the homology in both settings. We will then motivate obstruction bundles through very natural examples of Morse functions and metrics which do not satisfy the Smale condition. The goal is to understand this gluing technique in a simpler set up and analyse Morse theory with assumptions weaker than Smale condition on surfaces. We can apply Obstruction bundle gluing introduced by Hutchings and Taubes in Embedded contact homology to the setting of Morse theory. This is work in progress with Yuan Yao.