The Arnold-Givental conjecture and moment Floer homology

Details The Arnold-Givental conjecture and moment Floer homology The Arnold-Givental conjecture and moment Floer homology

2003-09-23

arxiv.org/abs/math/0309373v1

Mathematics

Symplectic Geometry

79 pages, 3 figures

Scientific paper

We prove the Arnold-Givental conjecture for a class of Lagrangian submanifolds in Marsden-Weinstein quotients which are fixpoint sets of some antisymplectic involution. For these Lagrangians the Floer homology cannot in general be defined by standard means due to the bubbling phenomenon. To overcome this difficulty we consider moment Floer homology whose boundary operator is defined by counting solutions of the symplectic vortex equations on the strip which have better compactness properties than the original Floer equations.

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