Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three

```@article{Hofer1993PseudoholomorphicCI,
title={Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three},
author={Helmut H. Hofer},
journal={Inventiones mathematicae},
year={1993},
volume={114},
pages={515-563}
}```
• H. Hofer
• Published 1 December 1993
• Mathematics
• Inventiones mathematicae
l. In t roduct ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 1.1. The Weinstein conjecture . . . . . . . . . . . . . . . . . . . . . . . . 515 1.2. The main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 1.3. Sketch of the proof . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 2. Local F redho lm theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 2.1. Similar i ty principle and consequences…
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References

SHOWING 1-10 OF 26 REFERENCES
Morse theory, the Conley index and Floer homology
In 1965 Arnold [1] conjectured that the number of fixed points of an exact symplectic diffeomorphism on a symplectic manifold M can be estimated below by the sum of the Betti numbers provided that
Geometry of Low-dimensional Manifolds: Filling by holomorphic discs and its applications
The survey is devoted to application of the technique of filling by holomorphic discs to different symplectic and complex analytic problems. COMPLEX AND SYMPLECTIC RECOLLECTIONS J -Convexity Let X, J
SOME GLOBAL PROPERTIES OF CONTACT STRUCTURES
transformations in general and to the study of global contact transformations in the special case of euclidean space. In attempting to generalize Lie's results to more general manifolds, it becomes
Classification of overtwisted contact structures on 3-manifolds
A contac t s t ructure on a (2n + l ) -d imensional manifold is a cod imens ion 1 tangent d is t r ibut ion which can be defined (at least locally) by a 1-form 7 with 7/x (d~)" nowhere 0. In this
Elliptic methods in symplectic geometry
The past few years have seen several exciting developments in the field of symplectic geometry, and a beginning has been made towards solving many important and hitherto inaccessible problems. The
Pseudo holomorphic curves in symplectic manifolds
Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called
The local behaviour of holomorphic curves in almost complex 4-manifolds
In this paper we prove various results about the positivity of intersections of holomorphic curves in almost complex 4-manifolds which were stated by Gromov. We also show that the virtual genus of
The unregularized gradient flow of the symplectic action
The symplectic action can be defined on the space of smooth paths in a symplectic manifold P which join two Lagrangian submanifolds of P. To pursue a new approach to the variational theory of this