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

Ekholm, Tobias¹

¹ Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

Geometry & topology, Tome 11 (2007) no. 2, pp. 1083-1224.

Résumé

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.

Détail

DOI : 10.2140/gt.2007.11.1083

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

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