New geometric structures on 3-manifolds: surgery and generalized geometry

Paper by J. Porti and R. Rubio.

Abstract: Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: B₃-generalized complex structures. We prove that any closed orientable 3-manifold admits such a structure, which can be chosen to be stable, that is, generically cosymplectic up to generalized diffeomorphism.

Find it on the arXiv (2402.12471).