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## Alexander polynomials for tanglesAdd to your list(s) Download to your calendar using vCal - Claudius Zibrowius (Cambridge)
- Friday 12 December 2014, 15:00-16:00
- MR13.
If you have a question about this talk, please contact Joe Waldron. Link Floer homology categorifies the multivariable 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. A simpler question to start with is, of course: What is the Alexander polynomial of a tangle? As it turns out, this is not entirely clear. There are several (a priori different) constructions to which I am going to add yet another one: In this talk, we consider a polynomial tangle invariant defined via generalised Kauffman states and Alexander codes. We will see that this invariant enjoys many properties of the classical multivariate Alexander polynomial, in particular invariance under mutation. We will then see how to interpret the tangle invariant geometrically. Finally, I will talk about how to make the transition to the Heegaard Floer world in the hope of defining a categorified version and, if time permits, ideas to make this construction glueable. This talk is part of the Junior Geometry Seminar series. ## This talk is included in these lists:- All CMS events
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