Augmentations are sheaves for Legendrian graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2019
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909807103967232 |
|---|---|
| author | An, Byung Hee Bae, Youngjin Su, Tao |
| author_facet | An, Byung Hee Bae, Youngjin Su, Tao |
| contents | In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital $A_{\infty}$-category, which lifts the set of augmentations of the associated Chekanov-Eliashberg DGA, and a DG category of constructible sheaves on the front plane, with micro-support at contact infinity controlled by the (bordered) Legendrian graph. In other words, generalizing [21], we prove "augmentations are sheaves" in the singular case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_10782 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Augmentations are sheaves for Legendrian graphs An, Byung Hee Bae, Youngjin Su, Tao Symplectic Geometry Algebraic Topology Geometric Topology Primary: 57R17, Secondary: 57M15, 14F05 In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital $A_{\infty}$-category, which lifts the set of augmentations of the associated Chekanov-Eliashberg DGA, and a DG category of constructible sheaves on the front plane, with micro-support at contact infinity controlled by the (bordered) Legendrian graph. In other words, generalizing [21], we prove "augmentations are sheaves" in the singular case. |
| title | Augmentations are sheaves for Legendrian graphs |
| topic | Symplectic Geometry Algebraic Topology Geometric Topology Primary: 57R17, Secondary: 57M15, 14F05 |
| url | https://arxiv.org/abs/1912.10782 |