On Bott-Morse Foliations and their Poisson Structures in Dimension 3

Abstract

We show that a Bott-Morse foliation in dimension 3 admits a linear, singular, Poisson structure of rank 2 with Bott-Morse singularities. We provide the Poisson bivectors for each type of singular component, and compute the symplectic forms of the characteristic distribution.

arXiv comment15 pages, 1 figure

References in corpus (2)

• On the connectedness of the space of codimension one foliations on a closed 3-manifold
• Poisson structures on smooth 4-manifolds

Cited by in corpus (5)

• Homotopy types of diffeomorphism groups of polar Morse-Bott foliations on lens spaces, 1
• On Computational Poisson Geometry II: Numerical Methods
• On Computational Poisson Geometry I: Symbolic Foundations
• Diffeomorphism groups of Morse-Bott foliation on the solid Klein bottle by Klein bottles parallel to the boundary
• Vector bundle automorphisms preserving Morse-Bott foliations