Obstructions for Symplectic Lie Algebroids

[摘要] 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.

[关键词] Poisson geometry;Lie algebroids;log-symplectic;elliptic symplectic 2020 Mathematics Subject Classification 53D17;53D05