Generalized Contact Bundles

TL;DR

This paper introduces a line bundle framework for odd-dimensional generalized contact structures, unifying existing theories and clarifying their geometric and algebraic properties through Lie algebroids and groupoids.

Contribution

It presents a novel approach that unifies all existing generalized contact structures and clarifies their integrability conditions using Lie algebroids and groupoids.

Findings

Unified framework for generalized contact structures

Clear geometric interpretation of integrability conditions

Connection to Lie algebroids and groupoids

Abstract

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.