Journal of Symplectic Geometry

Volume 15 (2017)

Number 1

Equivalences of coisotropic submanifolds

Pages: 107 – 149

DOI: http://dx.doi.org/10.4310/JSG.2017.v15.n1.a4

Authors

Florian Schätz (Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Aarhus, Denmark)

Marco Zambon (Department of Mathematics, KU Leuven, Belgium)

Abstract

We study the role that Hamiltonian and symplectic diffeomorphisms play in the deformation problem of coisotropic submanifolds. We prove that the action by Hamiltonian diffeomorphisms corresponds to the gauge-action of the $L_{\infty}$-algebra of Oh and Park. Moreover we introduce the notion of extended gauge-equivalence and show that in the case of Oh and Park’s $L_{\infty}$-algebra one recovers the action of symplectic isotopies on coisotropic submanifolds. Finally, we consider the transversally integrable case in detail.

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