Work

Hypersymplectic Structures Invariant Under an Effective Circle Action

Year: 2025

Type: article

Abstract: A hypersymplectic structure on a 4-manifold is a triple of symplectic forms for which any non-zero linear combination is again symplectic. In 2006, Donaldson [5] conjectured that on a compact 4-manifold any hypersymplectic structure can be deformed through cohomologous hypersymplectic structures to a hyperkähler triple. We prove this under the assumption that the initial structure is invariant under an effective $S^{1}$-action. In particular, we show that the underlying 4-manifold is diffeomorphic to $\mathbb{T}^{4}$.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf252

Authors: Joel Fine, Weiyong He, Chengjian Yao

Institutions: Université Libre de Bruxelles, University of Oregon, ShanghaiTech University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G1753454774