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• W3197162619 abstract "We introduce a new approach to universal quantum knot invariants that emphasizes generating functions instead of generators and relations. All the relevant generating functions are shown to be perturbed Gaussians of the form $Pe^G$, where $G$ is quadratic and $P$ is a suitably restricted perturbation. After developing a calculus for such Gaussians in general we focus on the rank one invariant $mathbf{Z}_mathbb{D}$ in detail. We discuss how it dominates the $mathfrak{sl}_2$-colored Jones polynomials and relates to knot genus and Whitehead doubling. In addition to being a strong knot invariant that behaves well under natural operations on tangles $mathbf{Z}_mathbb{D}$ is also computable in polynomial time in the crossing number of the knot. We provide a full implementation of the invariant and provide a table in an appendix." @default.
• W3197162619 created "2021-09-13" @default.
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• W3197162619 date "2021-09-05" @default.
• W3197162619 modified "2023-09-27" @default.
• W3197162619 title "Perturbed Gaussian generating functions for universal knot invariants" @default.
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