# Vera Vertesi (University of Strasbourg)

## Combinatorial Tangle Floer homology

Knot Floer homology is an invariant for knots and links defined by Ozsvath and Szabo and independently by Rasmussen. It has proven to be a powerful invariant e.g. in computing the genus of a knot, or determining whether a knot is fibered. In this talk I give a combinatorial generalisation of knot Floer homology for tangles; Tangle Floer homology is an invariant of tangles in $$D^3$$, $$S^2\times I$$ or in $$S^3$$. Tangle Floer homology satisfies a gluing theorem and its version in $$S^3$$ gives back a stabilisation of knot Floer homology. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin-Turaev invariant for $$\mathfrak{gl}(1|1)$$. This is a joint work with Ina Petkova and Alexander Ellis.