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 Poincare 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.

This is the version published by Geometry & Topology on 8 December 2006

References in corpus (4)

• Contact homology and one parameter families of Legendrian knots
• Knots and Contact Geometry
• The nonuniqueness of Chekanov polynomials of Legendrian knots
• Legendrian knots and links classified by classical invariants

Cited by in corpus (15)

• A Duality Exact Sequence for Legendrian Contact Homology
• Generating families and Legendrian contact homology in the standard contact space
• Floer theory for Lagrangian cobordisms
• Lagrangian Cobordisms via Generating Families: Constructions and Geography
• The nonuniqueness of Chekanov polynomials of Legendrian knots
• Augmentations are Sheaves
• Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families
• Product Structures for Legendrian Contact Homology
• Bilinearised Legendrian contact homology and the augmentation category
• Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
• A Legendrian Turaev torsion via generating families
• Legendrian Contact Homology in Seifert Fibered Spaces
• Duality and kernels in microlocal geometry
• Non-fillable augmentations of twist knots
• Calabi-Yau structure on the Chekanov-Eliashberg algebra of a Legendrian sphere