On a polynomial Alexander invariant for tangles (and its categorification)
Claudius Zibrowius (University of Cambridge)
Wednesday 15th July, 2015 16:00-17:00 Maths 325
Link Floer homology categorifies the multivariate Alexander polynomial, a classical invariant for knots and links. Motivated by constructions in Khovanov homology, one can ask if it is possible to define this invariant “locally”, i.e. to generalise it to tangles.
In the first part of this talk, we generalise the Kauffman state formula for the classical multivariate Alexander polynomial of knots and links to tangles and thereby obtain a finite set of polynomial tangle invariants. They enjoy many properties of the classical multivariate Alexander polynomial, in particular invariance under Conway mutation, and also allow a geometric interpretation. In the second part of the talk, we define a homological tangle invariant via sutured Floer homology whose graded Euler characteristic agrees with the polynomial tangle invariant.