The Alexander Polynomial as a Reshetikhin-Turaev Invariant

Jonathan Grant (Durham University)

Monday 27th October, 2014 16:00-17:00 Maths 326

Abstract

The Alexander polynomial is a classical invariant of knots introduced in the 1920's with clear connections to the topology of knots and surfaces. The Reshetikhin-Turaev invariants are much more recent, and are in general much more poorly understood. These often arise from the representation theory of quantum groups. I will show how the Alexander polynomial can be interpreted as a Reshetikhin-Turaev invariant using representations of U_q(gl(1|1)), and show how this can be used to understand a category of representations of U_q(gl(1|1)). Finally, I will give some suggestions about how this should tie into categorifications of knot invariants, and particularly the connection between HOMFLY homology and Heegaard Floer knot homology.

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