Exotic symplectic manifolds from Lefschetz fibrations

Abstract

In this paper we construct, in all odd complex dimensions, pairs of Liouville domains W_0 and W_1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W_0 is symplectically very similar to the cotangent bundle itself, W_1 is more unusual. We use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W_1 is trivial. As a corollary we obtain that W_1 contains no compact exact Lagrangian submanifolds.

31 pages, 6 figures. Substantially rewritten and updated

References in corpus (5)

• Functors and Computations in Floer homology with Applications Part II
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• On manifolds with corners
• Altering symplectic manifolds by homologous recombination
• The symplectic geometry of cotangent bundles from a categorical viewpoint

Cited by in corpus (6)

• Dehn twists and free subgroups of symplectic mapping class groups
• Legendrian Fronts for Affine Varieties
• Distinguishing between exotic symplectic structures
• Exotic families of symplectic manifolds with Milnor fibers of $ADE$-type
• Lefschetz fibrations on cotangent bundles and some plumbings
• Non-standard Symplectic Structures via Symplectic Cohomology