Obstructions for Symplectic Lie Algebroids

Ralph L. Klaasse

Symmetry, integrability and geometry: methods and applications, Tome 16 (2020)

Résumé

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.

Détail

Keywords: Poisson geometry, log-symplectic, elliptic symplectic.
Mots-clés : Lie algebroids

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