The geometry of graded cotangent bundles

Abstract

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^{\ast }[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical structures, such as higher Courant algebroids on $A\oplus {\bigwedge }^{k-1}{A}^{\ast }$ and higher Dirac structures therein, semi-direct products of Lie algebroid structures on $A$ with their coadjoint representations up to homotopy, and branes on certain AKSZ $\sigma$-models.

28 pages

References in corpus (7)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Supergroupoids, double structures, and equivariant cohomology
• H-twisted Lie algebroids
• On higher analogues of Courant algebroids
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• QP-Structures of Degree 3 and 4D Topological Field Theory
• L_infinity algebras as 1-jets of simplicial manifolds (and a bit beyond)