Floer homology of three manifolds and applications to low dimensional topology

23 September - 16 December 2024

Mondays, 10:15 - 12:00

Location: HG G 43 (exception: 23 and 30 Sept. in HG G 19.2)

First lecture: 23 September

Abstract

Floer homology and the related invariants of 4-manifolds has given us deep insight in smooth differential topology in dimensions 3 and particularly 4. The theory has yielded insights like existence of exotic differentiable structures on 4 dimensional euclidean space, complex curves minimize genus in complex projective space, killing the Hauptvermuntung, there even appear to be connection to the 4 color map theorem. This course will build up Floer homology of three manifolds from scratch. The focus will be on Instanton Floer homology but we will mention other versions and develop applications as the course goes on.