Volume 11, issue 2 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Morse flow trees and Legendrian contact homology in 1–jet spaces

Tobias Ekholm

Geometry & Topology 11 (2007) 1083–1224

arXiv: math/0509386

Abstract

Let L J1(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 TM, with boundary on the projection of L and asymptotic to the double points of this projection at punctures, provided n 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