Orbifolds as diffeologies
微分几何
2010-04-16 v3 几何拓扑
摘要
We consider orbifolds as diffeological spaces. This gives rise to a natural notion of differentiable maps between orbifolds, making them into a subcategory of diffeology. We prove that the diffeological approach to orbifolds is equivalent to Satake's notion of a V-manifold and to Haefliger's notion of an orbifold. This follows from a lemma: a diffeomorphism (in the diffeological sense) of finite linear quotients lifts to an equivariant diffeomorphism.
引用
@article{arxiv.math/0501093,
title = {Orbifolds as diffeologies},
author = {Patrick Iglesias and Yael Karshon and Moshe Zadka},
journal= {arXiv preprint arXiv:math/0501093},
year = {2010}
}
备注
26 pages, 6 figures. Minor changes.