A refined functorial universal tangle invariant

Jorge Becerra

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arXiv · 2501.17668

A refined functorial universal tangle invariant

Jorge Becerra

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Abstract

The universal invariant with respect to a given ribbon Hopf algebra is a tangle invariant that dominates all the Reshetikhin-Turaev invariants built from the representation theory of the algebra. We construct a canonical strict monoidal functor that encodes the universal invariant of upwards tangles and refines the Kerler-Kauffman-Radford functorial invariant. Moreover, this functor preserves the braiding, twist and the open trace, the latter being a mild modification of Joyal-Street-Verity's notion of trace in a balanced category. We construct this functor using the more flexible XC-algebras, a class which contains both ribbon Hopf algebras and endomorphism algebras of representation of these.

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Jorge Becerra. 2025-01-29. A refined functorial universal tangle invariant. https://arxiv.org/abs/2501.17668

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