TL;DR
This paper proves a generalized version of Morton's formula, enabling the expression of colored Jones polynomials of cable knots in terms of the original knot's polynomials, thus advancing computational techniques in knot theory.
Contribution
The paper introduces a generalized Morton's formula that relates colored Jones polynomials of cable knots to those of the original knot, providing a new computational tool.
Findings
Generalized Morton's formula proved.
Colored Jones polynomials of cable knots expressed in terms of original knot.
Enhanced methods for knot polynomial calculations.
Abstract
In this paper, a generalized version of Morton's formula is proved. Using this formula, one can write down the colored Jones polynomials of cabling of an knot in terms of the colored Jones polynomials of the original knot.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Numerical Analysis Techniques · semigroups and automata theory