PreprintCC BY 4.0arXiv
Triangulation of orbifolds with corners
Abstract
We prove that every compact orbifold with corners admits a triangulation in which the image of every codimension one face is a subcomplex. Faces need not be embedded, and the local groups may permute boundary components. The proof turns the boundary hyperplanes of linear charts into mirrors by means of the squaring map, which, unlike the folding y↦|y|, is compatible with smooth changes of charts, and then applies the triangulation theorem for orbit spaces of proper Lie groupoids.
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BibTeX
@misc{yu2026triangulation,
title = {{Triangulation of orbifolds with corners}},
author = {Hao Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31001},
eprint = {2610.31001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31001},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triangulation of orbifolds with corners
AU - Hao Yu
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31001
UR - https://arxiv.org/abs/2610.31001
AB - We prove that every compact orbifold with corners admits a triangulation in which the image of every codimension one face is a subcomplex. Faces need not be embedded, and the local groups may permute boundary components. The proof turns the boundary hyperplanes of linear charts into mirrors by means of the squaring map, which, unlike the folding y↦|y|, is compatible with smooth changes of charts, and then applies the triangulation theorem for orbit spaces of proper Lie groupoids.
ER -