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Symplectic Geometry
These are lecture notes for two courses, taught at the University of Toronto in Spring 1998 and in Fall 2000. Our main sources have been the books " Symplectic Techniques " by Guillemin-Sternberg and
From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds
A beautiful and comprehensive introduction to this important field. --Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment
Symplectic hypersurfaces and transversality in Gromov-Witten theory
We use Donaldson hypersurfaces to construct pseudo-cycles which define Gromov-Witten invariants for any symplectic manifold which agree with the invariants in the cases where transversality could be
The symplectic vortex equations and invariants of Hamiltonian group actions
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is
Handle attaching in symplectic homology and the Chord Conjecture
Abstract.Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a characteristic chord with respect to any contact form. I confirm this conjecture
In this paper we construct the Floer homology for an action functional which was introduced by Rabinowitz and prove a vanishing theorem. As an application, we show that there are no displaceable
J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions
3 Invariants of Hamiltonian group actions 17 3.1 An action functional . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Symplectic reduction . . . . . . . . . . . . . . . . . . . . . . . 19 3.3
Rabinowitz Floer homology and symplectic homology
The Rabinowitz-Floer homology groups $RFH_*(M,W)$ are associated to an exact embedding of a contact manifold $(M,\xi)$ into a symplectic manifold $(W,\omega)$. They depend only on the bounded
The role of string topology in symplectic field theory
We outline a program for incorporating holomorphic curves with Lagrangian boundary conditions into symplectic field theory, with an emphasis on ideas, geometric intuition, and a description of the