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

TL;DR

The paper introduces coisotropic Luttinger surgery, a new method to construct infinitely many symplectic 6-manifolds with vanishing canonical class that are not simple products, expanding the toolkit for symplectic geometry.

Contribution

It generalizes Luttinger surgery to higher dimensions and produces novel examples of symplectic 6-manifolds with zero first Chern class that are not product manifolds.

Findings

Constructed infinitely many non-Kahler symplectic 6-manifolds with c1=0

Demonstrated the generalization of Luttinger surgery to coisotropic submanifolds

Provided new examples outside known product constructions

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.