Morse flow trees and Legendrian contact homology in 1–jet spaces

Ekholm, Tobias

doi:10.2140/gt.2007.11.1083

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Morse flow trees and Legendrian contact homology in 1–jet spaces

Tobias Ekholm

Geometry & Topology 11 (2007) 1083–1224

DOI: 10.2140/gt.2007.11.1083

arXiv: math/0509386

Abstract

Let $L \subset J^{1} (M)$ 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 pseudo-holomorphic disks in $T^{*} M$ , with boundary on the projection of $L$ and asymptotic to the double points of this projection at punctures, provided $n \leq 2$ , or provided $n > 2$ and the front of $L$ has only cusp edge singularities. This result, in particular, shows how to compute the Legendrian contact homology of $L$ in terms of Morse theory.

Keywords

holomorphic disk, Morse theory, flow tree, contact homology, Legendrian, Lagrangian

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 53D40

References

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Publication

Received: 20 September 2005

Revised: 1 January 2007

Accepted: 20 February 2007

Published: 30 May 2007

Proposed: Eleny Ionel

Seconded: Yasha Eliashberg and Leonid Polterovich

Authors

Tobias Ekholm
Department of Mathematics Uppsala University Box 480 751 06 Uppsala Sweden

Volume 11, issue 2 (2007)