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In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of the integrability condition for generalized contact structures; (3) in light of new results on multiplicative forms and Spencer operators, it allows a simple interpretation of the defining equations of a generalized contact structure in terms of Lie algebroids and Lie groupoids.
Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting
A Jacobi structure $J$ on a line bundle $Lto M$ is weakly regular if the sharp map $J^sharp : J^1 L to DL$ has constant rank. A generalized contact bundle with regular Jacobi structure possess a transverse complex structure. Paralleling the work of B
Motivated by the computations done in cite{C1}, where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category $mathsf{Bun}_{G,M}$ of principal $G$-bundles over
We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction applies in the contact and l.c.s. settings. The BFV-complex of a coisotropic submanifold $S$ co
A nice differential-geometric framework for (non-abelian) higher gauge theory is provided by principal 2-bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local trivializations are kinds of Morita equivalences, and c