String nets for twisted pivotal categories
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910266985283584 |
|---|---|
| author | Haïoun, Benjamin Stewart, William Sytilidis, Filippos |
| author_facet | Haïoun, Benjamin Stewart, William Sytilidis, Filippos |
| contents | We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism Hypothesis.
This graphical calculus depends on a possibly singular foliation, and we use it to construct twisted string net modules for surfaces equipped with a Morse function or a Morse foliation. We prove that, despite the apparent dependence on this Morse function, the twisted string net modules assemble in an oriented categorified 2-TQFT.
We study when the twisted string net module of the 2-sphere vanishes, relate it to the distinguished invertible object for finite tensor categories and exhibit examples of non-unimodular finite tensor categories with non-vanishing twisted string net module on the 2-sphere. This vanishing is expected to be the main obstruction for extending our categorified 2-TQFT to a non-compact 3-TQFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | String nets for twisted pivotal categories Haïoun, Benjamin Stewart, William Sytilidis, Filippos Quantum Algebra Category Theory Geometric Topology 57K16, 18M20 We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism Hypothesis. This graphical calculus depends on a possibly singular foliation, and we use it to construct twisted string net modules for surfaces equipped with a Morse function or a Morse foliation. We prove that, despite the apparent dependence on this Morse function, the twisted string net modules assemble in an oriented categorified 2-TQFT. We study when the twisted string net module of the 2-sphere vanishes, relate it to the distinguished invertible object for finite tensor categories and exhibit examples of non-unimodular finite tensor categories with non-vanishing twisted string net module on the 2-sphere. This vanishing is expected to be the main obstruction for extending our categorified 2-TQFT to a non-compact 3-TQFT. |
| title | String nets for twisted pivotal categories |
| topic | Quantum Algebra Category Theory Geometric Topology 57K16, 18M20 |
| url | https://arxiv.org/abs/2605.28650 |