PhD Thesis: Shifted Contact Structures on Differentiable Stacks
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915219402391552 |
|---|---|
| author | Maglio, Antonio |
| author_facet | Maglio, Antonio |
| contents | This thesis focuses on developing "stacky" versions of contact structures, extending the classical notion of contact structures on manifolds. A fruitful approach is to study contact structures using line bundle-valued $1$-forms. Specifically, we introduce the notions of $0$ and $+1$-shifted contact structures on Lie groupoids. To define the kernel of a line bundle-valued $1$-form $θ$ on a Lie groupoid, we draw inspiration from the concept of the homotopy kernel in Homological Algebra. That kernel is essentially given by a representation up to homotopy (RUTH). Similarly, the curvature is described by a specific RUTH morphism. Both the definitions are motivated by the Symplectic-to-Contact Dictionary, which establishes a relationship between Symplectic and Contact Geometry. Examples of $0$-shifted contact structures can be found in contact structures on orbifolds, while examples of $+1$-shifted contact structures include the prequantization of $+1$-shifted symplectic structures and the integration of Dirac-Jacobi structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PhD Thesis: Shifted Contact Structures on Differentiable Stacks Maglio, Antonio Differential Geometry Mathematical Physics Symplectic Geometry 22A22, 53D10, 53D17, 18N50 This thesis focuses on developing "stacky" versions of contact structures, extending the classical notion of contact structures on manifolds. A fruitful approach is to study contact structures using line bundle-valued $1$-forms. Specifically, we introduce the notions of $0$ and $+1$-shifted contact structures on Lie groupoids. To define the kernel of a line bundle-valued $1$-form $θ$ on a Lie groupoid, we draw inspiration from the concept of the homotopy kernel in Homological Algebra. That kernel is essentially given by a representation up to homotopy (RUTH). Similarly, the curvature is described by a specific RUTH morphism. Both the definitions are motivated by the Symplectic-to-Contact Dictionary, which establishes a relationship between Symplectic and Contact Geometry. Examples of $0$-shifted contact structures can be found in contact structures on orbifolds, while examples of $+1$-shifted contact structures include the prequantization of $+1$-shifted symplectic structures and the integration of Dirac-Jacobi structures. |
| title | PhD Thesis: Shifted Contact Structures on Differentiable Stacks |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry 22A22, 53D10, 53D17, 18N50 |
| url | https://arxiv.org/abs/2503.24238 |