Deformations of symplectic cohomology and exact Lagrangians in ALE spaces

Details Deformations of symplectic cohomology and exact Lagrangians in ALE spaces Deformations of symplectic cohomology and exact Lagrangians in ALE spaces

2009-03-02

arxiv.org/abs/0903.0240v2

GAFA (Geometric And Functional Analysis) vol.20 n.3 (2010) pp.779-816

Mathematics

Symplectic Geometry

35 pages, 3 figures, minor changes and corrected typos

Scientific paper

10.1007/s00039-010-0074-7

We prove that the only exact Lagrangian submanifolds in an ALE space are
spheres. ALE spaces are the simply connected hyperkahler manifolds which at
infinity look like C^2/G for any finite subgroup G of SL(2,C). They can be
realized as the plumbing of copies of the cotangent bundle of a 2-sphere
according to ADE Dynkin diagrams. The proof relies on symplectic cohomology.

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