Duality for Legendrian contact homology

Abstract

The main result of this paper is that, off of a “fundamental class” in degree $1$, the linearized Legendrian contact homology obeys a version of Poincaré duality between homology groups in degrees $k$ and $-k$. Not only does the result itself simplify calculations, but its proof also establishes a framework for analyzing cohomology operations on the linearized Legendrian contact homology.