A fast polynomial-time knot invariant pair (Δ, θ) with superior distinguishing power on small knots, a genus bound, and simpler formulas for a previously studied quantity.
A cabling formula for the 2-loop polynomial of knots
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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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2025 1verdicts
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A Fast, Strong, Topologically Meaningful and Fun Knot Invariant
A fast polynomial-time knot invariant pair (Δ, θ) with superior distinguishing power on small knots, a genus bound, and simpler formulas for a previously studied quantity.