Simultaneous deformations and Poisson geometry

Abstract

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications can not be, to our knowledge, obtained by other methods such as operad theory.

32 pages. Results in Section 2 improved (Lemma 2.6 and Corollaries 2.20, 2.22). Corollary 2.5 and Corollary 2.11 added. Final version, accepted for publication

References in corpus (2)

• Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
• Deformations of coisotropic submanifolds for fibrewise entire Poisson structures

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• Jacobi bundles and the BFV-complex
• A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
• Split Courant algebroids as $L_{\infty }$-structures
• Stability of fixed points of Dirac structures
• Stability and rigidity of 3-Lie algebra morphisms