Coisotropic branes in symplectic manifolds

Abstract

A brane in a symplectic manifold is a coisotropic submanifold $Y$ endowed with a compatible closed 2-form $F$, which together induce a transverse complex structure. For a specific class of branes we give an explicit description of branes nearby a given one, and for arbitrary branes we describe the infinitesimal deformations and provide an associated cochain complex. As an application, we determine to what extent coisotropic submanifolds near a given brane admit brane structures.

arXiv commentv2: Added Remark 4.20 on the obstruction map, Example 4.2, Lemma 4.22 and Lemma 4.25. Final version accepted for publication. 34 pages