Simultaneous deformations and Poisson geometry
Quantum Algebra
2016-06-30 v3 Mathematical Physics
Algebraic Topology
math.MP
Symplectic 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.
Cite
@article{arxiv.1202.2896,
title = {Simultaneous deformations and Poisson geometry},
author = {Yael Fregier and Marco Zambon},
journal= {arXiv preprint arXiv:1202.2896},
year = {2016}
}
Comments
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