Gauge theoretic invariants and bypass exact triangles

Thomas Hockenhull (Max Planck Institute for Mathematics)

Monday 24th October, 2022 16:00-17:00 Maths 311B

Abstract

There are a host of different, powerful invariants for three-manifolds of various types coming from gauge theory, and most of these are known to satisfy a so-called ‘bypass exact triangle’ for versions which see contact geometric information. I will give an overview of this and describe how, in the case of three-manifolds-with-torus-boundary, the existence of these exact triangles predicts the existence of corresponding ‘bordered minus’ invariants. At its root, this can be seen as a completely algebraic statement about (partially) wrapped Fukaya categories of various punctured surfaces, so the talk should also be of some interest to those so inclined.

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