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Odd knot invariants from quantum covering groups

Sean Clark

Algebraic & Geometric Topology 17 (2017) 2961–3005
Abstract

We show that the quantum covering group associated to osp(1|2n) has an associated colored quantum knot invariant à la Reshetikhin–Turaev, which specializes to a quantum knot invariant for osp(1|2n), and to the usual quantum knot invariant for so(1 + 2n). In particular, this furnishes an “odd” variant of so(1 + 2n) quantum invariants, even for knots labeled by spin representations. We then show that these knot invariants are essentially the same, up to a change of variables and a constant factor depending on the knot and weight.

Keywords
quantum groups, knot invariants, Lie superalgebra
Mathematical Subject Classification 2010
Primary: 17B37, 57M27
References
Publication
Received: 18 October 2016
Revised: 28 February 2017
Accepted: 9 May 2017
Published: 19 September 2017
Authors
Sean Clark
Department of Mathematics
Northeastern University
Boston, MA
United States
https://web.northeastern.edu/sclark/