All Link Invariants for Two Dimensional Solutions of Yang-Baxter Equation and Dressings

Details All Link Invariants for Two Dimensional Solutions of Yang-Baxter Equation and Dressings All Link Invariants for Two Dimensional Solutions of Yang-Baxter Equation and Dressings

2006-12-27

arxiv.org/abs/math/0612781v1

JKTR 15 (2006) 1279-1301

Mathematics

Geometric Topology

24 pages, 16 figures

Scientific paper

10.1142/S0218216506005147

All polynomial invariants of links for two dimensional solutions of Yang-Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there exist three solutions connecting to the Alexander polynomial. Invariants for higher dimensional solutions, obtained by the so-called dressings, are also investigated. It is observed that the dressings do not improve link invariant unless some restrictions are put on dressed solutions.

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