Regular Bundles on Orbifolds: A Short Proof of Presentability
Abstract
Let X be a Hausdorff second-countable smooth orbifold without boundary, possibly noncompact and ineffective. Suppose dimX≤ n and |Gx|≤ B for integers n≥0 and B≥1, where Gx is the full stabilizer at x. We construct a smooth Hermitian bundle of explicit rank R(n,B) whose fibre at x is a positive multiple of C[Gx]. Adams operations cancel the Bott obstructions on the boundary spheres of a locally finite good triangulation, and the connectivity of Stiefel manifolds gives actual bundles representing the resulting virtual classes. Smoothing preserves all stabilizer representations. Unitary frames give X≃[M/U(R(n,B))] for a smooth manifold M with a proper locally free action; M is compact exactly when |X| is compact. Thus every compact smooth orbifold is presentable.
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BibTeX
@misc{becerra2026regular,
title = {{Regular Bundles on Orbifolds: A Short Proof of Presentability}},
author = {Enrique Becerra and Ernesto Lupercio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.08125},
eprint = {2609.08125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08125},
}
RIS
TY - UNPB
TI - Regular Bundles on Orbifolds: A Short Proof of Presentability
AU - Enrique Becerra
AU - Ernesto Lupercio
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.08125
UR - https://arxiv.org/abs/2609.08125
AB - Let X be a Hausdorff second-countable smooth orbifold without boundary, possibly noncompact and ineffective. Suppose dimX≤ n and |G_x|≤ B for integers n≥0 and B≥1, where G_x is the full stabilizer at x. We construct a smooth Hermitian bundle of explicit rank R(n,B) whose fibre at x is a positive multiple of C[G_x]. Adams operations cancel the Bott obstructions on the boundary spheres of a locally finite good triangulation, and the connectivity of Stiefel manifolds gives actual bundles representing the resulting virtual classes. Smoothing preserves all stabilizer representations. Unitary frames give X≃[M/U(R(n,B))] for a smooth manifold M with a proper locally free action; M is compact exactly when |X| is compact. Thus every compact smooth orbifold is presentable.
ER -