On Auroux's Luttinger-surgery uniqueness question

Abstract

We construct simply connected integral symplectic four-manifolds forming an exotic pair, with equal values of $c_1^2$, $c_2$, $c_1\cdot [\omega ]$, and $[\omega {]}^2$, but with symplectic Kodaira dimensions $-\infty$ and $2$. Since symplectic Kodaira dimension is invariant under Luttinger surgery, the two manifolds are not Luttinger-surgery equivalent. This gives a negative answer to Auroux's uniqueness question.

arXiv comment8 pages