Excision of Skein Categories and Factorisation Homology

Abstract

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.

arXiv comment38 pages, 15 figures

References in corpus (5)

• Factorization homology of topological manifolds
• Integrating quantum groups over surfaces
• Perturbative algebraic quantum field theory
• Skein theory for SU(n)-quantum invariants
• Higher categories, colimits, and the blob complex

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• Categorical Center of Higher Genera and 4D Factorization Homology
• Stated skein algebras and their representations
• Mapping Class Group Representations Derived from Stated Skein Algebras
• The ${\mathfrak{gl}}_2$-Skein Module of Lens Spaces via the Torus and Solid Torus