Quantum Invariants of Ribbon Surfaces in $4$-Dimensional $2$-Handlebodies
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908718163034112 |
|---|---|
| author | Beliakova, Anna De Renzi, Marco Faes, Quentin |
| author_facet | Beliakova, Anna De Renzi, Marco Faes, Quentin |
| contents | We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$-dimensional $2$-handlebodies up to $1$-isotopy. In the process, we recover invariants due to Bobtcheva-Messia, Broda-Petit, Gainutdinov-Geer-Patureau-Runkel (in collaboration with the second author), and Lee-Yetter. Our approach does not assume semisimplicity, and is based on a generalization of the Reshetikhin-Turaev functor to the category of labeled Kirby graphs which also yields invariants of framed links in the boundary of $4$-dimensional $2$-handlebodies up to $2$-deformations. The setup is very flexible, and allows for several different constructions, using central elements satisfying equations introduced by Hennings and Bobtcheva-Messia, modified traces, and modules over Frobenius algebras satisfying conditions dictated by the diagrammatic calculus for embedded surfaces developed by Hughes, Kim, and Miller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Invariants of Ribbon Surfaces in $4$-Dimensional $2$-Handlebodies Beliakova, Anna De Renzi, Marco Faes, Quentin Geometric Topology Quantum Algebra We use unimodular ribbon categories to construct quantum invariants of ribbon surfaces in $4$-dimensional $2$-handlebodies up to $1$-isotopy. In the process, we recover invariants due to Bobtcheva-Messia, Broda-Petit, Gainutdinov-Geer-Patureau-Runkel (in collaboration with the second author), and Lee-Yetter. Our approach does not assume semisimplicity, and is based on a generalization of the Reshetikhin-Turaev functor to the category of labeled Kirby graphs which also yields invariants of framed links in the boundary of $4$-dimensional $2$-handlebodies up to $2$-deformations. The setup is very flexible, and allows for several different constructions, using central elements satisfying equations introduced by Hennings and Bobtcheva-Messia, modified traces, and modules over Frobenius algebras satisfying conditions dictated by the diagrammatic calculus for embedded surfaces developed by Hughes, Kim, and Miller. |
| title | Quantum Invariants of Ribbon Surfaces in $4$-Dimensional $2$-Handlebodies |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2512.15395 |