A note on coherent orientations for exact Lagrangian cobordisms

Cecilia Karlsson
University of Oslo, Norway

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Abstract

Let be a spin, exact Lagrangian cobordism in the symplectization of the 1-jet space of a smooth manifold. Assume that has cylindrical Legendrian ends. It is well known that the Legendrian contact homology of can be defined with integer coefficients, via a signed count of pseudo-holomorphic disks in the cotangent bundle of. It is also known that this count can be lifted to a mod 2 count of pseudo-holomorphic disks in the symplectization, and that induces a morphism between the-valued DGA

of the ends in a functorial way. We prove that this hold with integer coefficients as well.

The proofs are built on the technique of orienting the moduli spaces of pseudo-holomorphic disks using capping operators at the Reeb chords. We give an expression for how the DGA

change if we change the capping operators.

Cite this article

Cecilia Karlsson, A note on coherent orientations for exact Lagrangian cobordisms. Quantum Topol. 11 (2020), no. 1, pp. 1–54

DOI 10.4171/QT/132

Dates

Submitted: 11 December 2017
Accepted: 7 January 2019
Published: 19 October 2019

Identifiers

DOI: 10.4171/QT/132

Keywords

Exact Lagrangian cobordism
Legendrian contact homology
orientations of moduli spaces

Mathematics Subject Classification