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 universal U(1)-RCC invariant of links and rationality conjecture
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abstract
We define a graph algebra version of the stationary phase integration over the coadjoint orbits in the Reshetikhin formula for the colored Jones-HOMFLY polynomial. As a result, we obtain a `universal' U(1)-RCC invariant of links in rational homology spheres, which determines the U(1)-RCC invariants based on simple Lie algebras. We formulate a rationality conjecture about the structure of this invariant.
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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.