An L-infinity structure for Legendrian contact homology
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913947044544512 |
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| author | Ng, Lenhard |
| author_facet | Ng, Lenhard |
| contents | For any Legendrian knot or link in $\mathbb{R}^3$, we construct an $L_\infty$ algebra that can be viewed as an extension of the Chekanov-Eliashberg differential graded algebra. The $L_\infty$ structure incorporates information from rational Symplectic Field Theory and can be formulated combinatorially. One consequence is the construction of a Poisson bracket on commutative Legendrian contact homology, and we show that the resulting Poisson algebra is an invariant of Legendrian links under isotopy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An L-infinity structure for Legendrian contact homology Ng, Lenhard Symplectic Geometry Geometric Topology 53D42, 53D10, 53D12, 55P50, 57K10, 57K43 For any Legendrian knot or link in $\mathbb{R}^3$, we construct an $L_\infty$ algebra that can be viewed as an extension of the Chekanov-Eliashberg differential graded algebra. The $L_\infty$ structure incorporates information from rational Symplectic Field Theory and can be formulated combinatorially. One consequence is the construction of a Poisson bracket on commutative Legendrian contact homology, and we show that the resulting Poisson algebra is an invariant of Legendrian links under isotopy. |
| title | An L-infinity structure for Legendrian contact homology |
| topic | Symplectic Geometry Geometric Topology 53D42, 53D10, 53D12, 55P50, 57K10, 57K43 |
| url | https://arxiv.org/abs/2311.14614 |