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.

15 pages, 1 figure