Vera Vertesi: Tangle Floer homology

In this talk I give a TQFT-type description of knot Floer homology by generalising it to tangles. Tangle Floer homology is an invariant of tangles in \(D^3\), \(S^2\times I\) or \(S^3\), which satisfies a pairing theorem and its version in \(S^3\) gives back a stabilisation of knot Floer homology. This invariant is also an extension of knot Floer homology as the categorification of the Alexander polynomial: Tangle Floer homology is a lift of the \(gl(1|1)\)- Reshetikhin—Turaev invariant defining the Alexander polynomial.
 
This is a joint work with  Alexander P. Ellis and Ina Petkova.