Mathematics Seminar
Date: Monday, 6 November 2023.
Time: 2:00 - 3:00 PM
Venue: Lecture Hall 2
Tight contact structures on Seifert fibered 3-manifolds
Tanushree Shah
Alfréd Rényi Institute, Hungary.
06-11-23

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Abstract

I will start by introducing contact structures. They come in two flavors: tight and overtwisted. Classification of overtwisted contact structures is well understood as opposed to tight contact structures. Tight contact structures have been classified on some 3 manifolds like S^3, R^3, Lens spaces, toric annuli, and almost all Seifert fibered manifolds with 3 exceptional fibers. We look at classification on one example of the Seifert fibered manifold with 4 exceptional fibers. I will explain the Legendrian surgery and convex surface theory which help us calculate the lower bound and upper bound of a number of tight contact structures. We will look at what more classification results can we hope to get using the same techniques and what is far-fetched.