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

2024/02/19 by Joan Porti, Roberto Rubio, Porti, Joan +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2402.12471

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.

Citations

• The Geometries of 3-Manifolds

Related

• An Almost Contact Structure on G₂-Manifolds
• Round surgery and contact structures on 3-manifolds
• Contact topology and CR geometry in three dimensions
• Generalized almost contact structures and generalized Sasakian structures
• From complex contact structures to real almost contact 3-structures