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SUMMARY:Alexander polynomials​ for tangles - Claudius Zibrowius (Cambrid
 ge)
DTSTART:20141212T150000Z
DTEND:20141212T160000Z
UID:TALK56673@talks.cam.ac.uk
CONTACT:Joe Waldron
DESCRIPTION:Link Floer homology categorifies the ​multivariable Alexande
 r polynomial\, a classical invariant for knots and links. Motivated by con
 structions 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 \nAlexander polynomial 
 of a tangle?  As it turns out\, this is not entirely clear.​\n \n​Ther
 e are several (a priori different) constructions to which I am going to ad
 d yet another one: In this talk\, we consider a polynomial tangle invarian
 t defined via generalised Kauffman states and Alexander codes.  We will se
 e that​ this invariant enjoys ​many properties of the classical​ mul
 tivariate ​Alexander polynomial\, in particular invariance under mutatio
 n. We will then see how to interpret the tangle invariant geometrically. F
 inally\, I will talk about how to make the transition to the Heegaard Floe
 r world in the hope of defining a categorified version and\, if time permi
 ts\, ideas to make this construction glueable​.
LOCATION:MR13
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