# On twisted contact groupoids and on integration of twisted Jacobi manifolds

## TL;DR

This paper introduces twisted contact groupoids, explores their role in integrating twisted Jacobi manifolds, and examines their relationships with twisted Poisson and symplectic structures, supported by examples.

## Contribution

It extends the theory of contact and symplectic groupoids to include twisted structures and studies their integration of twisted Jacobi manifolds.

## Key findings

- Introduction of twisted contact groupoids
- Connection between twisted Jacobi and twisted Poisson manifolds
- Examples illustrating each structure

## Abstract

We introduce the concept of twisted contact groupoids, as an extension either of contact groupoids or of twisted symplectic ones, and we discuss the integration of twisted Jacobi manifolds by twisted contact groupoids. We also investigate the very close relationships which link homogeneous twisted Poisson manifolds with twisted Jacobi manifolds and homogeneous twisted symplectic groupoids with twisted contact ones. Some examples for each structure are presented.