Duality for Legendrian contact homology

Sabloff, Joshua M

doi:10.2140/gt.2006.10.2351

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Duality for Legendrian contact homology

Joshua M Sabloff

Geometry & Topology 10 (2006) 2351–2381

DOI: 10.2140/gt.2006.10.2351

arXiv: math.SG/0508187

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.

Keywords

contact homology, legendrian knot, duality

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 53D12, 53D40, 57M25

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Publication

Received: 7 September 2005

Revised: 29 July 2006

Accepted: 9 November 2006

Published: 8 December 2006

Proposed: Yasha Eliashberg

Seconded: Leonid Polterovich, Joan Birman

Authors

Joshua M Sabloff
Haverford College Haverford, PA 19041 USA

Volume 10, issue 4 (2006)