English

Torsion in linearized contact homology for Legendrian knots

Symplectic Geometry 2024-07-18 v2 Geometric Topology

Abstract

We present examples of Legendrian knots in R3\mathbb{R}^3 that have linearized Legendrian contact homology over Z\mathbb{Z} containing torsion. As a consequence, we show that there exist augmentations of Legendrian knots over Z\mathbb{Z} that are not induced by exact Lagrangian fillings, even though their mod 22 reductions are.

Keywords

Cite

@article{arxiv.2308.13482,
  title  = {Torsion in linearized contact homology for Legendrian knots},
  author = {Robert Lipshitz and Lenhard Ng},
  journal= {arXiv preprint arXiv:2308.13482},
  year   = {2024}
}

Comments

19 pages, 7 figures. V2: minor revisions; accepted for publication in Michigan Math. J