Morse flow trees and Legendrian contact homology in 1–jet spaces
- 30 May 2007
- journal article
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 11 (2), 1083-1224
- https://doi.org/10.2140/gt.2007.11.1083
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 $T^\ast M$, 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
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