English

A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}

Symplectic Geometry 2014-01-28 v5

Abstract

We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact homology under this relation. The result about the Thurston-Bennequin number can be considered as a generalization of the result of Chantraine which holds when n = 1. In addition, we provide a few constructions of Lagrangian cobordisms and prove that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian n-tori in R^{2n+1}.

Keywords

Cite

@article{arxiv.1108.3693,
  title  = {A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}},
  author = {Roman Golovko},
  journal= {arXiv preprint arXiv:1108.3693},
  year   = {2014}
}

Comments

14 pages, 2 figures; improved exposition, many minor corrections, this version has been accepted for publication in the Pacific Journal of Mathematics