Deformations of Symplectic Cohomology and Exact Lagrangians in ALE Spaces
Identifieur interne : 000443 ( Main/Exploration ); précédent : 000442; suivant : 000444Deformations of Symplectic Cohomology and Exact Lagrangians in ALE Spaces
Auteurs : Alexander F. Ritter [États-Unis, Royaume-Uni]Source :
- Geometric and Functional Analysis [ 1016-443X ] ; 2010-09-01.
English descriptors
Abstract
Abstract: ALE spaces are the simply connected hyperkähler manifolds which at infinity look like $${\mathbb{C}^{2}/G}$$, for any finite subgroup $${G \subset SL_2(\mathbb{C})}$$. We prove that all exact Lagrangians inside ALE spaces must be spheres. The proof relies on showing the vanishing of a twisted version of symplectic cohomology. This application is a consequence of a general deformation technique. We construct the symplectic cohomology for non-exact symplectic manifolds, and we prove that if the non-exact symplectic form is sufficiently close to an exact one then the symplectic cohomology coincides with an appropriately twisted version of the symplectic cohomology for the exact form.
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DOI: 10.1007/s00039-010-0074-7
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