Georgios Dimitroglou Rizell: Floer homology for Lagrangian cobordisms

Legendrian contact homology (LCH) is a Legendrian isotopy invariant. We introduce a version of wrapped Floer homology for pairs of Lagrangian cobordisms having Legendrian ends that admit augmentations.
This theory is used to establish long exact sequences involving the singular homology of a Lagrangian cobordism and the linearised LCH of its Legendrian ends. As an application we show that an exact Lagrangian cobordism from a Legendrian sphere to itself necessarily is a concordance in high dimensions. This is joint work with B. Chantraine, P. Ghiggini and R. Golovko.