Asian Journal of Mathematics

Volume 20 (2016)

Number 3

Deformations of coisotropic submanifolds in locally conformal symplectic manifolds

Pages: 553 – 596

DOI: http://dx.doi.org/10.4310/AJM.2016.v20.n3.a7

Authors

Hông Vân Lê (Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic)

Yong-Geun Oh (Center for Geometry and Physics, Institute for Basic Sciences, Namgu, Pohang, Korea; and Department of Mathematics, POSTECH, Pohang, Korea)

Abstract

In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive two equivalent equations that govern $C^{\infty}$ deformations of coisotropic submanifolds. Using the first equation we define the corresponding $C^{\infty}$-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. Secondly, we prove that the formal deformation problem is governed by an $L_{\infty}$-structure which is a $\mathfrak{b}$-deformation of strong homotopy Lie algebroids introduced in [OP] in the symplectic context. Then we study deformations of locally conformal symplectic structures and their moduli space. Using the second equation we study the corresponding bulk (extended) deformations of coisotropic submanifolds. Finally we revisit Zambon’s obstructed infinitesimal deformation [Za] in this enlarged context and prove that it is still obstructed.

Keywords

locally conformal symplectic manifold, coisotropic submanifold, $\mathfrak{b}$-twisted differential, bulk deformation, Zambon’s example

2010 Mathematics Subject Classification

53D35

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