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arXiv · 2509.07921

Bordered Legendrian Rational Symplectic Field Theory

Maciej Wlodek
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Abstract

Given a Legendrian knot $\Lambda \subset \mathbb{R}^3$ and a vertical line dividing the front projection of $\Lambda$ 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.

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Maciej Wlodek. 2025-09-09. Bordered Legendrian Rational Symplectic Field Theory. https://arxiv.org/abs/2509.07921

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