Flat principal 2-group bundles and flat string structures
Algebraic Topology
2025-10-16 v2 Category Theory
Abstract
For a weak 2-group, we construct a bicategory of flat 2-group bundles over differentiable stacks as a localization of a functor bicategory. This description is amenable to explicit geometric constructions. For example, we show that flat 2-group bundles can be described in terms of ordinary -bundles together with a trivialization of a certain 2-gerbe. This specializes to a characterization of flat string structures on vector bundles over differentiable stacks.
Keywords
Cite
@article{arxiv.2110.07571,
title = {Flat principal 2-group bundles and flat string structures},
author = {Daniel Berwick-Evans and Emily Cliff and Laura Murray and Apurva Nakade and Emma Phillips},
journal= {arXiv preprint arXiv:2110.07571},
year = {2025}
}
Comments
42 pages. The previous version of this paper was changed significantly and split into two articles: this one, and arxiv:2510.10773