The geometrization of N-manifolds of degree 2

JOURNAL OF GEOMETRY AND PHYSICS

卷:133

Article

Lean, M. Jotz¹ 

[1] Georg August Univ Gottingen, Math Inst, Gottingen, Germany

关键词: Graded manifolds;    Double vector bundles;    Linear Poisson structures;    Representations up to homotopy;   

DOI  :  10.1016/j.geomphys.2018.07.007

来源: Elsevier

【 摘 要 】

This paper describes an equivalence of the canonical category of N-manifolds of degree 2 with a category of involutive double vector bundles. More precisely, we show how involutive double vector bundles are in duality with double vector bundles endowed with a linear metric. We describe then how special sections of the metric double vector bundle that is dual to a given involutive double vector bundle are the generators of a graded manifold of degree 2 over the double base. We discuss how split Poisson N-manifolds of degree 2 are equivalent to self-dual representations up to homotopy and so, following Gracia-Saz and Mehta, to linear splittings of a certain class of VB-algebroids. In other words, the equivalence of categories above induces an equivalence between so called Poisson involutive double vector bundles, which are the dual objects to metric VB-algebroids, and Poisson N-manifolds of degree 2. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free