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

##### Authors
Ritter, Alexander F.
##### Description
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.
Comment: 35 pages, 3 figures, minor changes and corrected typos
##### Keywords
Mathematics - Symplectic Geometry, Mathematics - Differential Geometry, 53D40, 53D12