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arXiv · 2112.06797

Symplectomorphisms of some Weinstein 4-manifolds

Paul Hacking·Ailsa Keating
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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.

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Paul Hacking, Ailsa Keating. 2021-12-13. Symplectomorphisms of some Weinstein 4-manifolds. https://doi.org/10.2140/gt.2026.30.645

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