Coisotropic Luttinger surgery and some new symplectic 6-manifolds with vanishing canonical class

Abstract

We introduce a surgery operation on symplectic manifolds called coisotropic Luttinger surgery, which generalizes Luttinger surgery on Lagrangian tori in symplectic 4-manifolds. We use it to produce infinitely many distinct symplectic non-Kahler 6-manifolds \(X\) with \(c_1(X)=0\) which are not of the form \(M\times F\) for \(M\) a symplectic 4-manifold and \(F\) a closed surface.