A note on Lagrangian cobordisms between Legendrian submanifolds of ℝ²ⁿ⁺¹

Roman Golovko

Vol. 261 (2013), No. 1, 101–116

DOI: 10.2140/pjm.2013.261.101

Abstract

We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of ℝ²ⁿ⁺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 ℝ²ⁿ⁺¹.

Keywords

Legendrian submanifold, Lagrangian cobordism, Thurston–Bennequin number, Legendrian contact homology

Mathematical Subject Classification 2010

Primary: 53D12

Secondary: 53D42

Milestones

Received: 6 December 2011

Revised: 16 July 2012

Accepted: 27 August 2012

Published: 28 February 2013