Exotic families of symplectic manifolds with Milnor fibers of $ADE$-type

TL;DR

This paper constructs infinitely many diffeomorphic Weinstein manifolds, including Milnor fibers of ADE-type and those formed by gluing cotangent bundles, with some having decomposable wrapped Fukaya categories.

Contribution

It introduces new infinite families of diffeomorphic Weinstein manifolds involving ADE-type Milnor fibers and cotangent bundle gluings, expanding the understanding of their symplectic structures.

Findings

Infinitely many diffeomorphic families of Weinstein manifolds constructed.

Milnor fibers of ADE-type are included in these families.

Some members have decomposable wrapped Fukaya categories.

Abstract

In this paper, we give infinitely many diffeomorphic families of different Weinstein manifolds. The diffeomorphic families consist of the Milnor fibers of $ADE$-type, and a Weinstein manifold constructed by gluing a cotangent bundle to the Milnor fiber of $A$-type. The last-mentioned members of the families have decomposable wrapped Fukaya categories.