# ORIENTATIONS IN LEGENDRIAN CONTACT HOMOLOGY AND EXACT LAGRANGIAN IMMERSIONS

@article{Ekholm2004ORIENTATIONSIL, title={ORIENTATIONS IN LEGENDRIAN CONTACT HOMOLOGY AND EXACT LAGRANGIAN IMMERSIONS}, author={Tobias Ekholm and John B. Etnyre and Michael G. Sullivan}, journal={International Journal of Mathematics}, year={2004}, volume={16}, pages={453-532} }

We show how to orient moduli spaces of holomorphic disks with boundary on an exact Lagrangian immersion of a spin manifold into complex n-space in a coherent manner. This allows us to lift the coefficients of the contact homology of Legendrian spin submanifolds of standard contact (2n + 1)-space from ℤ2 to ℤ. We demonstrate how the ℤ-lift provides a more refined invariant of Legendrian isotopy. We also apply contact homology to produce lower bounds on double points of certain exact Lagrangian…

## 93 Citations

### Legendrian Contact Homology

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A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P × R where P is an exact symplectic manifold is established. The class of such contact…

### Morse flow trees and Legendrian contact homology in 1-jet spaces

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- 2007

Let L ⊂ J 1 (M) be a Legendrian submanifold of the 1-jet space of a Riemannian n-manifold M. A correspondence is established between rigid flow trees in M determined by L and boundary punctured rigid…

### The orientability problem in open Gromov–Witten theory

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- 2013

We give an explicit formula for the holonomy of the orientation bundle of a family of real Cauchy‐Riemann operators. A special case of this formula resolves the orientability question for spaces of…

### Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold

- Mathematics
- 2013

We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in $S^1\times S^2$ or any connected sum $\#^k(S^1\times S^2)$, viewed as the contact…

### Legendrian contact homology in $P \times \mathbb{R}$

- Mathematics
- 2007

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P x R, where P is an exact symplectic manifold, is established. The class of such contact…

### Legendrian Contact Homology in P X R

- Mathematics
- 2005

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such…

### Exact Lagrangian immersions with a single double point

- Mathematics
- 2011

Let k > 2. We show that if a closed orientable 2k-manifold K, with Euler characteristic not equal to -2, admits an exact Lagrangian immersion into complex Euclidean 2k-space with one transverse…

### Rational SFT, Linearized Legendrian Contact Homology, and Lagrangian Floer Cohomology

- Mathematics
- 2009

We relate the version of rational symplectic field theory for exact Lagrangian cobordisms introduced in [6] to linearized Legendrian contact homology. More precisely, if L ⊂ Xis an exact Lagrangian…

### An exact sequence for Legendrian links

- Mathematics
- 2015

A result of Bourgeois, Ekholm and Eliashberg [4] describes the linearized contact homology of the boundary of a symplectic cobordism obtained by Legendrian surgery in terms of the cyclic homology of…

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