Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 121, 13 pages      arXiv:1811.05084      https://doi.org/10.3842/SIGMA.2020.121

Obstructions for Symplectic Lie Algebroids

Ralph L. Klaasse
Département de Mathematique, Université libre de Bruxelles, CP 218 Boulevard du Triomphe, B-1050 Bruxelles, Belgium

Received April 06, 2020, in final form November 23, 2020; Published online November 27, 2020

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.

Key words: Poisson geometry; Lie algebroids; log-symplectic; elliptic symplectic.

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