On Donaldson’s 4-6 question
Abstract
We prove that the examples of Smith (2000) and McMullen and Taubes (1999) provide infinitely many counterexamples to one direction of Donaldson's 4-6 question and the closely related stabilising conjecture.These are the first known counterexamples.In the other direction, we show that the Gromov-Witten invariants of two simply connected closed symplectic 4-manifolds agree if their products with .S 2 ; !std / are deformation equivalent.In particular, when b C 2 2, these 4-manifolds have the same Seiberg-Witten invariants.Furthermore, one can replace .S 2 ; !std / by .S 2 ; !std / k for any k 1 in both results.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometry and complex manifolds
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Geometry & Topology
- Volume
- 30
- Issue
- 8
- Pages
- 3145–3167
- Publication date
- 30 August 2026
- Language
- EN