Exactly solvable models and new link polynomials. II: Link polynomials for closed 3-braids. (English) Zbl 0719.57004
Summary: Using a generalized Alexander-Conway relation derived from a three-state exactly solvable model in statistical mechanics, new invariant polynomials for knots and links are explicitly evaluated. It is shown that the invariant polynomials for closed 3-braids are obtained recursively. It is also shown that the invariant polynomials are more powerful than the Jones polynomials.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
