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arXiv · 2609.26452

On Sections of Quotient maps by Isometries

Suyoung Choi·Tao Gong
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Abstract

Suppose that a discrete group $G$ acts smoothly, properly, and effectively on a connected smooth manifold $M$, and let $q:M\to M/G$ 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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Suyoung Choi, Tao Gong. 2026-09-22. On Sections of Quotient maps by Isometries. https://arxiv.org/abs/2609.26452

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