Solid torus links and Hecke algebras of \({\mathcal B}\)-type. (English) Zbl 0884.57004
Yetter, David N. (ed.), Proceedings of the conference on quantum topology, Manhattan, KS, USA, March 24–28, 1993. Singapore: World Scientific. 225-245 (1994).
Summary: We show how to construct a HOMFLY-PT type oriented link invariant for links inside a solid torus, following V. F. R. Jones’s original approach, i.e. via normalizing an Ocneanu-type linear trace function from the Hecke algebras of \({\mathcal B}\)-type to the complex numbers. Before defining the invariant we set up the appropriate topological theory, then we find the braid groups related to the solid torus and observe that these can be represented by the Hecke algebras of \({\mathcal B}\)-type. Finally we compare our invariant with a skein invariant for certain dichromatic links found by J. Hoste and M. E. Kidwell [Trans. Am. Math. Soc. 321, No. 1, 197-229 (1990; Zbl 0702.57002)].
For the entire collection see [Zbl 0869.00040].
For the entire collection see [Zbl 0869.00040].
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
