Obstructions for Symplectic Lie Algebroids

Abstract

Several types of generically-nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, $b^k$-, scattering and elliptic-log Poisson structures. In this paper we discuss topological obstructions to the existence of such Poisson structures, obtained through the characteristic classes of their associated symplectic Lie algebroids. In particular we obtain the full obstructions for surfaces to carry such Poisson structures.

References in corpus (10)

• Symplectic and Poisson geometry on b-manifolds
• Stable generalized complex structures
• Desingularizing $b^m$-symplectic structures
• Fibrations and log-symplectic structures
• Geometric structures and Lie algebroids
• Poisson structures of divisor-type
• Type one generalized Calabi--Yaus
• Fibrations and stable generalized complex structures
• Fold-Forms for Four-Folds
• Holomorphic curves in log-symplectic manifolds

Cited by in corpus (2)

• Poisson structures of divisor-type
• Log symplectic manifolds and $[Q,R]=0$