Remarks on the categorification of colored Jones polynomials
Noboru Ito
TL;DR
This paper introduces a new categorification of colored Jones polynomials for nanowords and constructs a Khovanov-type bicomplex with three grading levels.
Contribution
It extends the categorification framework to nanoword invariants and establishes a new bicomplex structure with multiple gradings.
Findings
Defined colored Jones polynomials for nanowords
Proved the existence of a three-graded Khovanov-type bicomplex
Enhanced understanding of categorification in knot theory
Abstract
We introduce colored Jones polynomials of nanowords and their categorification. We also prove the existence of a Khovanov-type bicomplex which has three grades.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Geometric and Algebraic Topology