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New geometric structures on 3-manifolds: surgery and generalized geometry (2402.12471v2)
Published 19 Feb 2024 in math.DG, math.GT, and math.SG
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: $B_3$-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.
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