An adelic extension of the Jones polynomial. (English) Zbl 1222.57010
Banagl, Markus (ed.) et al., The mathematics of knots. Theory and application. Berlin: Springer (ISBN 978-3-642-15636-6/hbk; 978-3-642-15637-3/ebook). Contributions in Mathematical and Computational Sciences 1, 125-142 (2011).
The authors represent classical braids in the Yokonuma-Hecke algebra and the adelic Yokonuma-Hecke algebra, in analogy to the \(p\)-adic framed braid and the \(p\)-adic Yokonuma-Hecke algebras defined in the article [J. Juyumaya and S. Lambropoulou, J. S. Carter et al. (eds.), Intelligence of low dimensional topology 2006, Hiroshima, Japan July 22–26, 2006. Hackensack, NJ: World Scientific. Series on Knots and Everything 40, 75–84 (2007; Zbl 1151.57002)]. Furthermore using the adelic Markov trace the authors construct topological invariants of classical knots and links. Each invariant satisfies a cubic skein relation coming from the Yokonuma-Hecke algebra. The authors provide some small sample computations and speculate that their invariants are different from the HOMFLYPT polynomial.
For the entire collection see [Zbl 1205.57002].
For the entire collection see [Zbl 1205.57002].
Reviewer: Claus Ernst (Bowling Green)
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 20C08 | Hecke algebras and their representations |
Citations:
Zbl 1151.57002References:
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