article

Title: Co-isotropic Luttinger surgery and some new examples of symplectic Calabi-Yau 6-Manifolds

Authors: Paul Kirk and Scott Baldridge

Issue: Volume 62 (2013), Issue 5, 1457-1471

Abstract:

$We introduce a new surgery operation on symplectic manifolds called coisotropic Luttinger surgery, which generalizes Luttinger surgery on Lagrangian tori in symplectic 4-manifolds [K.\:M. Luttinger, \textit{Lagrangian tori in \mathbb{R}^4}, J.\ Differential Geom. \textbf{42} (1995), no. 2., 220--228]. We use it to produce infinitely many distinct symplectic non-K\"ahler 6-manifolds $X$ with $c_1(X)=0$ which are not symplectomorphic to $M\times F$ for $M$ a symplectic 4-manifold and $F$ a closed surface.$