WEINSTEIN CONJECTURE AND GW-INVARIANTS

A Note On Weinstein Conjecture

In this article, we give new proofs on the some cases on Weinstein conjecture and get some new results on Weinstein conjecture.

ar X iv : d g - ga / 9 71 20 20 v 1 3 0 D ec 1 99 7 Weinstein Conjecture and GW Invariants

Pseudo-holomorphic Curves and the Weinstein Conjecture

Let S ⊂ (N,ω) be a hypersurface in a symplectic manifold. The characteristic distribution LS on S consists of the tangent vectors v ∈ TS such that i(v)ωS = 0, where ωS is the pull back of ω to S. The flow lines generated by a vector field in LS are called characteristics. S ⊂ (N,ω) is said to be of contact type if there is a 1-form α on S such that dα = ωS and α(v) 6= 0 for any v 6= 0 in LS. Th...

The Weinstein conjecture for stable Hamiltonian structures

We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian structure, and let R denote the associated Reeb vector field on Y . We prove that if Y is not a T2 -bundle over S1 , then R has a closed orbit. Along the way we prove...

On the Weinstein Conjecture in Higher Dimensions

The first break-through on this conjecture was obtained by C. Viterbo, [19], showing that compact energy surfaces in R2n of contact-type have periodic orbits. Extending Gromov’s theory of pseudoholomorphic curves, [3], to symplectized contact manifolds, H. Hofer, [4], related the Weinstein conjecture to the existence of certain pseudoholomorphic curves. He showed that in dimension three the Wei...