Volume 11, issue 2 (2007)

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

Tobias Ekholm

Geometry & Topology 11 (2007) 1083–1224
 arXiv: math/0509386
Abstract

Let $L\subset {J}^{1}\left(M\right)$ 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 ${T}^{\ast }M$, with boundary on the projection of $L$ and asymptotic to the double points of this projection at punctures, provided $n\le 2$, 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
Primary: 57R17
Secondary: 53D40