Orbifolds as diffeologies

关于profinite微分几何空间的几何学

On the geometry of profinite diffeological spaces

本文研究profinite微分几何空间的几何性质，涵盖切余切空间、微分形式、度量、联络、算子及上同调关系，统一了多种构造。

Diffeologies, Differential Spaces, and Symplectic Geometry

Diffeological and differential spaces are generalisations of smooth structures on manifolds. We show that the "intersection" of these two categories is isomorphic to Frölicher spaces, another generalisation of smooth structures. We then give examples of such spaces, as well as examples of diffeological and differential spaces that do not fall into this category. We apply the theory of diffeological spaces to differential forms on a geometric quotient of a compact Lie group. We show that the subcomplex of basic forms is isomorphic to the complex of diffeological forms on the geometric quotient.…

On diffeologies for power sets and measures

We consider a differential geometric setting on power sets and Borel algebras. Our chosen framework is based on diffeologies, and we make a link between the various diffeological structures that we propose, having in mind set-valued maps, relations, set-valued gradients, differentiable measures, and shape analysis. This work intends to establish rigorous properties on sample diffeologies that seem of interest to us.

Differentiability, Convenient Spaces and Smooth Diffeologies

We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient iff the space and the tangent fibres coincide. Some basic comments on the relation with manifolds are given.

局部凸空间上的微分同胚与分布的光滑乘法

Diffeologies on Locally Convex Spaces and Smooth Multiplication of Distributions

从微分同胚角度研究Hausdorff局部凸空间上的自然光滑结构，并应用于分布的非线性运算，给出Mackey完备性的几何刻画，构造微局域可乘分布空间并证明乘法光滑。

微分几何黎曼orbifolds

Diffeological Riemannian orbifolds

研究可微栈上黎曼度量与微分几何轨道空间上黎曼度量数据的等价性，使用特定框架，证明经典黎曼orbifold与黎曼微分几何orbifold概念等价，还探讨李群胚上黎曼度量诱导条件及恰当性条件。