Deformations of Symplectic Cohomology and Exact Lagrangians in ALE Spaces

ALE spaces are the simply connected hyperkähler manifolds which at infinity look like ${mathbb{C}^{2}/G}ALE spaces are the simply connected hyperk?hler manifolds which at infinity look like mathbbC²/G{mathbb{C}^{2}/G}, for any finite subgroup G ì SL₂(mathbbC){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.