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Compactness results in Symplectic Field Theory
This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in (4). We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic…
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Finite energy foliations of tight three-spheres and Hamiltonian dynamics
Surfaces of sections are a classical tool in the study of 3-dimensional dynamical systems. Their use goes back to the work of Poincare and Birkhoff. In the present paper we give a natural…
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Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory
In this paper we start with the applications of polyfold theory to symplectic field theory.
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Properties of Pseudoholomorphic Curves in Symplectisations Iv: Asymptotics with Degeneracies
We study pseudoholomorphic maps ~ u = (a; u): _ S ! R M de-ned on punctured Riemannian surfaces, satisfying T ~ u i = ~ J T ~ u, with a special almost complex structure ~ J associated with a contact…
A General Fredholm Theory II: Implicit Function Theorems
Abstract.This is the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. In general, these spaces are not locally homeomorphic to open…
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A characterisation of the tight three-sphere
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Applications of symplectic homology I
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Applications of symplectic homology II: Stability of the action spectrum
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A general Fredholm theory I: A splicing-based differential geometry
This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. These spaces, in general, are locally not homeomorphic to open sets in…
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Finite energy cylinders of small area
\widetilde{J}-holomorphic cylinders in \mathbb{R}\times M, where M is a contact manifold are investigated. It is shown that a sufficiently long cylinder having small area is close to a constant map,…
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