Continuous and coherent actions on wrapped Fukaya categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910529779400704 |
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| author | Oh, Yong-Geun Tanaka, Hiro Lee |
| author_facet | Oh, Yong-Geun Tanaka, Hiro Lee |
| contents | We establish the continuous functoriality of wrapped Fukaya categories with respect to Liouville automorphisms, yielding a way to probe the homotopy type of the automorphism group of a Liouville sector. These methods prove Liouville and monotone cases of a conjecture of Teleman from the 2014 ICM. In the case of a cotangent bundle, we show that the Abouzaid equivalence between the wrapped category and the infinity-category of local systems intertwines our action with the action of diffeomorphisms of the zero section. In particular, our methods yield a typically non-trivial map from the rational homotopy groups of Liouville automorphisms to the rational string topology algebra of the zero section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_00349 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Continuous and coherent actions on wrapped Fukaya categories Oh, Yong-Geun Tanaka, Hiro Lee Symplectic Geometry Algebraic Topology We establish the continuous functoriality of wrapped Fukaya categories with respect to Liouville automorphisms, yielding a way to probe the homotopy type of the automorphism group of a Liouville sector. These methods prove Liouville and monotone cases of a conjecture of Teleman from the 2014 ICM. In the case of a cotangent bundle, we show that the Abouzaid equivalence between the wrapped category and the infinity-category of local systems intertwines our action with the action of diffeomorphisms of the zero section. In particular, our methods yield a typically non-trivial map from the rational homotopy groups of Liouville automorphisms to the rational string topology algebra of the zero section. |
| title | Continuous and coherent actions on wrapped Fukaya categories |
| topic | Symplectic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/1911.00349 |