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

N. Aizawa; M. Harada; M. Kawaguchi; E. Otsuki

doi:10.1142/s0218216506005147

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

N. Aizawa·M. Harada·M. Kawaguchi·E. Otsuki

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Abstract

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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N. Aizawa, M. Harada, M. Kawaguchi, E. Otsuki. 2006-12-27. All Link Invariants for Two Dimensional Solutions of Yang-Baxter Equation and Dressings. https://doi.org/10.1142/s0218216506005147

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