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arXiv · 1506.00339

Towards effective topological field theory for knots

A. Mironov·A. Morozov
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Abstract

Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on the structure of those mysterious formulas. Explicit expressions are now combined from Racah matrices of the type $R\otimes R\otimes\bar R\longrightarrow \bar R$ and mixing matrices in the sectors $R^{\otimes 3}\longrightarrow Q$. Further extension is provided by composition rules, allowing to glue two blocks, connected by an m-strand braid (they generalize the product formula for ordinary composite knots with m=1).

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A. Mironov, A. Morozov. 2015-06-12. Towards effective topological field theory for knots. https://doi.org/10.1016/j.nuclphysb.2015.08.005

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