A refined functorial universal tangle invariant
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908415446482944 |
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| author | Becerra, Jorge |
| author_facet | Becerra, Jorge |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A refined functorial universal tangle invariant Becerra, Jorge Geometric Topology Quantum Algebra 16T05, 18M10, 18M15, 57K10 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. |
| title | A refined functorial universal tangle invariant |
| topic | Geometric Topology Quantum Algebra 16T05, 18M10, 18M15, 57K10 |
| url | https://arxiv.org/abs/2501.17668 |