Equivalences of coisotropic submanifolds (Q2358617)

The paper is concerned with the deformation problem of coisotropic submanifolds which is a generalization of that of Lagrangian submanifolds. The authors introduce the notion of Hamiltonian equivalence among coisotropic sections and investigate a moduli space of coisotropic sections by the Hamiltonian equivalences, called the Hamiltonian moduli space of coisotropic sections. They show that there is a bijection between the Hamiltonian moduli space of coisotropic sections and a moduli space of Maurer-Cartan elements by gauge equivalences, basing on the results by \textit{Y.-G. Oh} and \textit{J.-S. Park} [Invent. Math. 161, No. 2, 287--360 (2005; Zbl 1081.53066)] and the authors [Lett. Math. Phys. 103, No. 7, 777--791 (2013; Zbl 1282.53073)]. Moreover, it is proved that every \(L_\infty\)-algebra from \textit{T. Voronov}'s derived bracket construction [J. Pure Appl. Algebra 202, No. 1--3, 133--153 (2005; Zbl 1086.17012)] is associated with additional automorphisms. Using the result, they introduce the notion of extended gauge equivalence among Maurer-Cartan elements and show that there is a bijection between a moduli space of coisotropic sections by symplectic isotopies and that of Maurer-Cartan elements by extended gauge equivalences. Lastly, they discuss the case where a given coisotropic submanifold is transversally integrable and give an explicit formula of a coisotropic deformation for it.