Parabolic skein modules

David Jordan; Jennifer Brown

Parabolic skein modules

School of Mathematics

Research output: Working paper › Preprint

Abstract

We develop skein theory for 3-manifolds in the presence of codimension-one defects, focusing especially on defects arising from parabolic induction/restriction for quantum groups. We use these defects as a model for the quantum decorated character stacks of arXiv:2102.12283, thus extending them to 3-manifolds with surface defects. As a special case we obtain knot invariants closely related to the "quantum A-polynomial", and we give a concrete method for computation resembling the approach of Dimofte and collaborators based on ideal triangulations and gluing equations.

Original language	English
Publisher	ArXiv
Publication status	Published - 1 May 2025

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https://arxiv.org/abs/2505.14836Licence: Creative Commons: Attribution (CC-BY)

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AB - We develop skein theory for 3-manifolds in the presence of codimension-one defects, focusing especially on defects arising from parabolic induction/restriction for quantum groups. We use these defects as a model for the quantum decorated character stacks of arXiv:2102.12283, thus extending them to 3-manifolds with surface defects. As a special case we obtain knot invariants closely related to the "quantum A-polynomial", and we give a concrete method for computation resembling the approach of Dimofte and collaborators based on ideal triangulations and gluing equations.

M3 - Preprint

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Parabolic skein modules

Abstract

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