Exotic Families of Symplectic Manifolds with Milnor Fibers of ADE-type
Joint work with Dongwook Choa, Sangjin Lee
Preprint arXiv:2111.08166
We give infinitely many diffeomorphic families of different Weinstein manifolds. The diffeomorphic families consist of the Milnor fibres of ADE-type, and a Weinstein manifold constructed by gluing a cotangent bundle to a Milnor fiber of A-type. The last mentioned members of the families have decomposable wrapped Fukaya categories. We use their Lefschetz fibrations to show that they are diffeomorphic (using Maydanskiy-Seidel). Then, we study their wrapped Fukaya categories/symplectic cohomologies and show that they are both non-vanishing but also not equivalent. This shows that they are not Weinstein homotopic.