On Bott-Morse Foliations and their Poisson structures in dimension three

M. Evangelista-Alvarado, P. Suárez-Serrato, J. Torres Orozco, and R. Vera

Journal of Singularities
volume 19 (2019), 19-33

Received: 4 September 2018.

DOI: 10.5427/jsing.2019.19b

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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.

Author(s) information:

M. Evangelista-Alvarado
Instituto de Matemáticas - Universidad Nacional Autónoma de México
Circuito Exterior, Ciudad Universitaria
Coyoacán, 04510
Mexico City, Mexico
email: miguel.eva.alv@matem.unam.mx

P. Suárez-Serrato
Department of Mathematics
University of California Santa Barbara, CA, USA
On leave from:
Instituto de Matemáticas - Universidad Nacional Autónoma de México
Circuito Exterior, Ciudad Universitaria
Coyoacán, 04510
Mexico City, Mexico
email: pablo@im.unam.mx

J. Torres Orozco
Centro de Ciencias Matemáticas
Antigua Carretera a Pátzcuaro 8701
Col. Ex Hacienda San José de la Huerta, 58089
Morelia, Michoacán, Mexico}
email: jonatan@cimat.mx

R. Vera
Instituto de Matemáticas - Universidad Nacional Autónoma de México
Circuito Exterior, Ciudad Universitaria
Coyoacán, 04510
Mexico City, Mexico
and
Department of Mathematics - KU Leuven
Celestijnenlaan 200B, B-3001
Leuven (Heverlee), Belgium
email: ramon.vera@kuleuven.be
email: rvera.math@gmail.com