Integration of 2-term representations up to homotopy via 2-functors
Differential Geometry
2016-08-03 v1
Abstract
Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid and we prove that the 1-truncation of this 2-groupoid is isomorphic to the Weinstein groupoid of the VB-algebroid associated to a representation up to homotopy. As applications, we describe alternative integration schemes for semi-direct products of Lie 2-algebras and string algebras.
Keywords
Cite
@article{arxiv.1608.00664,
title = {Integration of 2-term representations up to homotopy via 2-functors},
author = {Cristian Ortiz and Olivier Brahic},
journal= {arXiv preprint arXiv:1608.00664},
year = {2016}
}