Poly-Poisson Sigma models and their relational poly-symplectic groupoids
Abstract
The main idea of this note is to describe the integration procedure for poly-Poisson structures, that is, to find a poly-symplectic groupoid integrating a poly-Poisson structure, in terms of topological field theories, namely via the path-space construction. This will be given in terms of the poly-Poisson sigma model and we prove that every poly-Poisson structure has a natural integration via relational poly-symplectic groupoids, extending the results in [8] and [26]. We provide familiar examples (trivial, linear, constant and symplectic) within this formulation and we give some applications of this construction regarding the classification of poly-symplectic integrations, as well as Morita equivalence of poly-Poisson manifolds.
Cite
@article{arxiv.1706.06014,
title = {Poly-Poisson Sigma models and their relational poly-symplectic groupoids},
author = {Ivan Contreras and Nicolás Martínez Alba},
journal= {arXiv preprint arXiv:1706.06014},
year = {2018}
}
Comments
22 pages, 1 figure. Several typos and minor error fixed. A new section about applications was added