Excision for Spaces of Admissible Skeins
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911953626071040 |
|---|---|
| author | Runkel, Ingo Schweigert, Christoph Tham, Ying Hong |
| author_facet | Runkel, Ingo Schweigert, Christoph Tham, Ying Hong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Excision for Spaces of Admissible Skeins Runkel, Ingo Schweigert, Christoph Tham, Ying Hong Quantum Algebra 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. |
| title | Excision for Spaces of Admissible Skeins |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2407.09302 |