Towards a 2-dimensional notion of holonomy
Differential Geometry
2007-05-23 v3 Category Theory
Abstract
Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holonomy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for the crossed module case. The development also has to use corresponding notions for certain types of double groupoids. This leads to a holonomy Lie groupoid rather than double groupoid, but one which involves the 2-dimensional information.
Cite
@article{arxiv.math/0009082,
title = {Towards a 2-dimensional notion of holonomy},
author = {Ronald Brown and Ilhan Icen},
journal= {arXiv preprint arXiv:math/0009082},
year = {2007}
}
Comments
30 pages, A4, xypic, epic, eepic