论文标题
准类固醇和差异准则
Quasifold groupoids and diffeological quasifolds
论文作者
论文摘要
Quasifolds是通过可计数仿射组动作的$ \ Mathbb {r}^n $的商在本地建模的空间。这些空间首先出现在Elisa Prato对Delzant Construction的概括中，特殊情况包括圆环上非理性线性流的叶片空间和Orbifolds。我们考虑了嵌入差异空间类别的差异学准夫子的类别，以及准群体类似物的生物，它们嵌入了lie clopoids，bibundles和bibundle形态的生物中。我们证明，限制了那些在局部可逆的形态，以及有效的quasifold群体，将Quasifold grouptoid带到其差异轨道空间是基础类别的等效性。这些结果完成并扩展了与Masrour Zoghi的早期工作。
Quasifolds are spaces that are locally modelled by quotients of $\mathbb{R}^n$ by countable affine group actions. These spaces first appeared in Elisa Prato's generalization of the Delzant construction, and special cases include leaf spaces of irrational linear flows on the torus, and orbifolds. We consider the category of diffeological quasifolds, which embeds in the category of diffeological spaces, and the bicategory of quasifold groupoids, which embeds in the bicategory of Lie groupoids, bibundles, and bibundle morphisms. We prove that, restricting to those morphisms that are locally invertible, and to quasifold groupoids that are effective, the functor taking a quasifold groupoid to its diffeological orbit space is an equivalence of the underlying categories. These results complete and extend earlier work with Masrour Zoghi.
