English

Equivalences of coisotropic submanifolds

Differential Geometry 2015-09-15 v2 Symplectic Geometry

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 LL_\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 LL_\infty-algebra one recovers the action of symplectic isotopies on coisotropic submanifolds. Finally, we consider the transversally integrable case in detail.

Keywords

Cite

@article{arxiv.1411.3227,
  title  = {Equivalences of coisotropic submanifolds},
  author = {Florian Schaetz and Marco Zambon},
  journal= {arXiv preprint arXiv:1411.3227},
  year   = {2015}
}

Comments

There is an overlap between the results presented in one of the main sections of the present note (Section 3) and the recent preprint ArXiv:1410.8446 by L\^e, Oh, Tortorella and Vitagliano (once specialized to the symplectic case). Final version accepted for publication. Results in Section 4.3 simplified, Appendix and references added