PreprintCC BY 4.0arXiv
On Sections of Quotient maps by Isometries
Abstract
Suppose that a discrete group G acts smoothly, properly, and effectively on a connected smooth manifold M, and let q:M→ M/G be the quotient map. We prove that if q admits a continuous section, then G is generated by reflections. We also establish converse results for dissecting reflections and give applications to Euclidean and lattice actions.
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BibTeX
@misc{choi2026sections,
title = {{On Sections of Quotient maps by Isometries}},
author = {Suyoung Choi and Tao Gong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26452},
eprint = {2609.26452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26452},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Sections of Quotient maps by Isometries
AU - Suyoung Choi
AU - Tao Gong
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26452
UR - https://arxiv.org/abs/2609.26452
AB - Suppose that a discrete group G acts smoothly, properly, and effectively on a connected smooth manifold M, and let q:M→ M/G be the quotient map. We prove that if q admits a continuous section, then G is generated by reflections. We also establish converse results for dissecting reflections and give applications to Euclidean and lattice actions.
ER -