Equivalences of coisotropic submanifolds

TL;DR

This paper explores the relationship between Hamiltonian and symplectic diffeomorphisms in deforming coisotropic submanifolds, linking gauge actions to $L_ abla$-algebra structures and examining special cases.

Contribution

It establishes the correspondence between Hamiltonian diffeomorphisms and gauge actions of an $L_ abla$-algebra, introducing extended gauge-equivalence and analyzing transversally integrable cases.

Findings

Hamiltonian diffeomorphisms correspond to gauge actions of Oh and Park's $L_ abla$-algebra.

Extended gauge-equivalence recovers symplectic isotopies on coisotropic submanifolds.

Detailed analysis of the transversally integrable case.

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.