A cabling formula for the 2-loop polynomial of knots
Tomotada Ohtsuki
TL;DR
This paper introduces a cabling formula for the 2-loop polynomial of knots, enabling calculations of this polynomial for complex knots like torus knots, advancing knot invariant computations.
Contribution
It presents a novel cabling formula for the 2-loop polynomial of knots, including explicit calculations for torus knots.
Findings
Derived a cabling formula for the 2-loop polynomial
Calculated the 2-loop polynomial for torus knots
Enhanced methods for knot invariant computation
Abstract
The 2-loop polynomial is a polynomial presenting the 2-loop part of the Kontsevich invariant of knots. We show a cabling formula for the 2-loop polynomial of knots. In particular, we calculate the 2-loop polynomial for torus knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics