2024/07/12 by Ingo Runkel, Christoph Schweigert, Runkel, Ingo +3 · 1 citation
Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2407.09302
openalex publication_date 2024/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The skein module for a d-dimensional manifold is a vector space spanned by embedded framed graphs decorated by a category A with suitable extra structure depending on the dimension d, modulo local relations which hold inside d-balls. For a full subcategory S of A, an S-admissible skein module is defined analogously, except that local relations for a given ball may only be applied if outside the ball at least one edge is coloured in S. In this paper we prove that admissible skein modules in any dimension satisfy excision, namely that the skein module of a glued manifold is expressed as a coend over boundary values on the boundary components glued together. We furthermore relate skein modules for different choices of S, apply our result to cylinder categories, and recover the relation to modified traces.