Floer theory for Lagrangian cobordisms

TL;DR

This paper develops a Floer homology framework for exact Lagrangian cobordisms in contact geometry, establishing exact sequences that connect Morse and contact homologies to explore their topological features.

Contribution

It introduces intersection Floer homology for Lagrangian cobordisms with augmentations, linking Morse and contact homologies and advancing understanding of their topology.

Findings

Derived exact sequences relating Morse and contact homologies.

Established Floer homology for Lagrangian cobordisms with augmentations.

Investigated topological properties of exact Lagrangian cobordisms.

Abstract

In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the cobordisms admit augmentations. From this theory we derive several exact sequences relating the Morse homology of an exact Lagrangian cobordism with the bilinearised contact homologies of its ends. These are then used to investigate the topological properties of exact Lagrangian cobordisms.