#### Volume 17, issue 5 (2017)

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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 $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left(1|2n\right)$ has an associated colored quantum knot invariant à la Reshetikhin–Turaev, which specializes to a quantum knot invariant for $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left(1|2n\right)$, and to the usual quantum knot invariant for $\mathfrak{s}\mathfrak{o}\left(1+2n\right)$. In particular, this furnishes an “odd” variant of $\mathfrak{s}\mathfrak{o}\left(1+2n\right)$ 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
##### 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/