English

Bordered Legendrian Rational Symplectic Field Theory

Symplectic Geometry 2025-09-10 v1

Abstract

Given a Legendrian knot ΛR3\Lambda \subset \mathbb{R}^3 and a vertical line dividing the front projection of Λ\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.

Keywords

Cite

@article{arxiv.2509.07921,
  title  = {Bordered Legendrian Rational Symplectic Field Theory},
  author = {Maciej Wlodek},
  journal= {arXiv preprint arXiv:2509.07921},
  year   = {2025}
}
R2 v1 2026-07-01T05:28:45.526Z