PreprintarXiv licencearXiv
Flat principal 2-group bundles on S2 and their holonomy
Abstract
Let 𝒢(G,A,α) be a discrete 2-group, given as the {categorical} extension of an ordinary group G by an abelian group A. We define principal 𝒢-bundles over a manifold in terms of Čech data over a good open cover. In the case of the manifold S2, we calculate this bicategory explicitly, and identify its 2-skeleton. We compare with the holonomy bicategory Fun(*/ / π≤ 2(S2), * / / 𝒢), and provide a concrete equivalence between the two.
Related
- Gauge Rigidity and Holonomy Classification of Time-Scaled Intertwining Cocycles on Hilbert Bundles
- Generalized Killing spinors as Lagrangian sections of principal spin bundles
- Ricci flows and bracket flows on twisted principal bundles
- Reduction of structure groups for noncommutative principal bundles
- Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal ℝ-bundles
BibTeX
@misc{cliff2026flat,
title = {{Flat principal 2-group bundles on $S^2$ and their holonomy}},
author = {Emily Cliff and Yves Lolelo and Sandrine St-Cyr},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10402},
eprint = {2610.10402},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10402},
}
RIS
TY - UNPB
TI - Flat principal 2-group bundles on S^2 and their holonomy
AU - Emily Cliff
AU - Yves Lolelo
AU - Sandrine St-Cyr
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10402
UR - https://arxiv.org/abs/2610.10402
AB - Let 𝒢(G,A,α) be a discrete 2-group, given as the {categorical} extension of an ordinary group G by an abelian group A. We define principal 𝒢-bundles over a manifold in terms of Čech data over a good open cover. In the case of the manifold S^2, we calculate this bicategory explicitly, and identify its 2-skeleton. We compare with the holonomy bicategory Fun(*/ / π_≤ 2(S^2), * / / 𝒢), and provide a concrete equivalence between the two.
ER -