Compatible poisson structures on fibered 5-manifolds

R. Flores-Espinoza; J. C. Ruíz-Pantaleón; Yu Vorobiev

doi:10.1007/s40590-018-0225-7

Compatible poisson structures on fibered 5-manifolds

R. Flores-Espinoza, J. C. Ruíz-Pantaleón^*, Yu Vorobiev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a 5-dimensional orientable fibered manifolds with 2-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.

Original language	English
Pages (from-to)	187-209
Number of pages	23
Journal	Boletin de la Sociedad Matematica Mexicana
Volume	26
Issue number	1
DOIs	https://doi.org/10.1007/s40590-018-0225-7
State	Published - 1 Mar 2020

Bibliographical note

Funding Information:
This work was partially supported by the Mexican National Council of Science and Technology (CONACyT), under research project CB-2013-219631.

Publisher Copyright:
© 2018, Sociedad Matemática Mexicana.

Keywords

Almost coupling tensors
Fiber bundles
Poisson connections
Poisson structures

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10.1007/s40590-018-0225-7

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abstract = "We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a 5-dimensional orientable fibered manifolds with 2-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.",

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AU - Ruíz-Pantaleón, J. C.

AU - Vorobiev, Yu

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Y1 - 2020/3/1

N2 - We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a 5-dimensional orientable fibered manifolds with 2-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.

AB - We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a 5-dimensional orientable fibered manifolds with 2-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.

KW - Almost coupling tensors

KW - Fiber bundles

KW - Poisson connections

KW - Poisson structures

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IS - 1

ER -

Compatible poisson structures on fibered 5-manifolds

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Keywords

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