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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.07921 |
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| _version_ | 1866908528021602304 |
|---|---|
| author | Wlodek, Maciej |
| author_facet | Wlodek, Maciej |
| contents | Given a Legendrian knot $Λ\subset \mathbb{R}^3$ and a vertical line dividing the front projection of $Λ$ into two halves, we construct a differential graded algebra associated to each half-knot. We then show that one may obtain the commutative algebra from Legendrian Rational Symplectic Field Theory as a pushout of the two bordered algebras. This construction extends the bordered Chekanov-Eliashberg differential graded algebra by incorporating disks with multiple positive punctures into the differential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bordered Legendrian Rational Symplectic Field Theory Wlodek, Maciej Symplectic Geometry Given a Legendrian knot $Λ\subset \mathbb{R}^3$ and a vertical line dividing the front projection of $Λ$ into two halves, we construct a differential graded algebra associated to each half-knot. We then show that one may obtain the commutative algebra from Legendrian Rational Symplectic Field Theory as a pushout of the two bordered algebras. This construction extends the bordered Chekanov-Eliashberg differential graded algebra by incorporating disks with multiple positive punctures into the differential. |
| title | Bordered Legendrian Rational Symplectic Field Theory |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2509.07921 |