Towards effective topological field theory for knots
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 R R R and mixing matrices in the sectors R 3 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).
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.