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