Relative Calabi-Yau structures and perverse schobers on surfaces
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912921473253376 |
|---|---|
| author | Christ, Merlin |
| author_facet | Christ, Merlin |
| contents | We give a treatment of relative Calabi--Yau structures on functors between $R$-linear stable $\infty$-categories, with $R$ any $\mathbb{E}_\infty$-ring spectrum, generalizing previous treatments in the setting of dg-categories. Using their gluing properties, we further construct relative Calabi--Yau structures on the global sections of perverse schobers, i.e. categorified perverse sheaves, on surfaces with boundary. We treat examples related to Fukaya categories and representation theory. In a related direction, we define the monodromy of a perverse schober parametrized by a ribbon graph on a framed surface and show that it forms a local system of stable $\infty$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16597 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relative Calabi-Yau structures and perverse schobers on surfaces Christ, Merlin Algebraic Geometry Algebraic Topology Representation Theory 18N60 We give a treatment of relative Calabi--Yau structures on functors between $R$-linear stable $\infty$-categories, with $R$ any $\mathbb{E}_\infty$-ring spectrum, generalizing previous treatments in the setting of dg-categories. Using their gluing properties, we further construct relative Calabi--Yau structures on the global sections of perverse schobers, i.e. categorified perverse sheaves, on surfaces with boundary. We treat examples related to Fukaya categories and representation theory. In a related direction, we define the monodromy of a perverse schober parametrized by a ribbon graph on a framed surface and show that it forms a local system of stable $\infty$-categories. |
| title | Relative Calabi-Yau structures and perverse schobers on surfaces |
| topic | Algebraic Geometry Algebraic Topology Representation Theory 18N60 |
| url | https://arxiv.org/abs/2311.16597 |