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arXiv · 1706.06014

Poly-Poisson Sigma models and their relational poly-symplectic groupoids

Ivan Contreras·Nicolás Martínez Alba
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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 $(PPSM)$ 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.

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Ivan Contreras, Nicolás Martínez Alba. 2017-11-14. Poly-Poisson Sigma models and their relational poly-symplectic groupoids. https://doi.org/10.1063/1.5016851

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