Excision of Skein Categories and Factorisation Homology

Juliet Cooke

Excision of Skein Categories and Factorisation Homology

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arxiv 1910.02630 v1 pith:AA3RBW5Z submitted 2019-10-07 math.QA

Juliet Cooke This is my paper · ORCID

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keywords skeincategoriesfactorisationhomologyexcisionalgebraallowsapplication

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We prove that the skein categories of Walker--Johnson-Freyd satisfy excision. This allows us to conclude that skein categories are $k$-linear factorisation homology and taking the free cocompletion of skein categories recovers locally finitely presentable factorisation homology. An application of this is that the skein algebra of a punctured surface related to any quantum group with generic parameter gives a quantisation of the associated character variety.

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Parabolic skein modules
math.QA 2025-05 conditional novelty 7.0 of 10

Parabolic defect skein theory yields a new, triangulation-based definition and computation of the quantum A-ideal of knots, matching known classical limits.

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