Year: 2026
Type: preprint
Abstract: We construct simply connected integral symplectic four-manifolds forming an exotic pair, with equal values of $c_1^2$, $c_2$, $c_1\mathbin{\cdot}[ω]$, and $[ω]^2$, 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.
Source: arXiv (Cornell University)
Author: Iida, Nobuo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214285127