Symplectomorphisms of some Weinstein 4-manifolds
Abstract
Let M be a Weinstein four-manifold mirror to Y\D for (Y,D) a log Calabi--Yau surface; intuitively, this is typically the Milnor fibre of a smoothing of a cusp singularity. We introduce two families of symplectomorphisms of M: Lagrangian translations, which we prove are mirror to tensors with line bundles; and nodal slide recombinations, which we prove are mirror to automorphisms of (Y,D). The proof uses a detailed compatibility between the homological and SYZ view-points on mirror symmetry. Together with spherical twists, these symplectomorphisms are expected to generate all autoequivalences of the wrapped Fukaya category of M which are compactly supported in a categorical sense. A range of applications is given.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Geometry & Topology
- Volume
- 30
- Issue
- 2
- Pages
- 645–699
- Publication date
- 16 March 2026
- Language
- EN