On Newton polytopes of Lagrangian augmentations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913237825486848 |
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| author | Capovilla-Searle, Orsola Casals, Roger |
| author_facet | Capovilla-Searle, Orsola Casals, Roger |
| contents | This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher-dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly simplifies arguments and also allows us to show that there exist Legendrian links with infinitely many non-orientable exact Lagrangian fillings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03888 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Newton polytopes of Lagrangian augmentations Capovilla-Searle, Orsola Casals, Roger Symplectic Geometry Combinatorics Geometric Topology 53D12, 57K33, 52B20 This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher-dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly simplifies arguments and also allows us to show that there exist Legendrian links with infinitely many non-orientable exact Lagrangian fillings. |
| title | On Newton polytopes of Lagrangian augmentations |
| topic | Symplectic Geometry Combinatorics Geometric Topology 53D12, 57K33, 52B20 |
| url | https://arxiv.org/abs/2306.03888 |