3 papers
math.SG2025
Hypersymplectic Structures Invariant Under an Effective Circle Action
Joel Fine, Weiyong He, Chengjian Yao
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 conjectured that on a…
math.DG2024
Seiberg-Witten equations in all dimensions
Joel Fine, Partha Ghosh
Starting with an -dimensional oriented Riemannian manifold with a Spin-c structure, we describe an elliptic system of equations which recover the Seiberg-Witten equations when $…
math.DG2024
Convergence of the hypersymplectic flow on with -symmetry
Joel Fine, Weiyong He, Chengjian Yao
A hypersymplectic structure on a 4-manifold is a triple of 2-forms for which every non-trivial linear combination is a symplectic form.…