Smooth Lie group actions are parametrized diffeological subgroups

A tangent bundle on diffeological spaces

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

Groups of tree automorphisms as diffeological groups

We consider certain groups of tree automorphisms as so-called diffeological groups. The notion of diffeology, due to Souriau, allows to endow non-manifold topological spaces, such as regular trees that we look at, with a kind of a differentiable structure that in many ways is close to that of a smooth manifold; a suitable notion of a diffeological group follows. We first study the question of what kind of a diffeological structure is the most natural to put on a regular tree in a way that the underlying topology be the standard one of the tree. We then proceed to consider the group of all auto…

商群的李代数

Lie algebras of quotient groups

研究商群$G/H$微分流到李代数的条件，并将经典不可积分巴纳赫-李代数整合到微分流群中。

李群模稠密子群的de Rham上同调

The de Rham cohomology of a Lie group modulo a dense subgroup

研究李群G模稠密子群H的de Rham上同调与李代数g/h的李代数上同调的关系，揭示其等价性。

横向平均算子与非闭子群商的上同调

A Transverse Averaging Operator and Cohomology of Quotients by Homogeneous Non-closed Subgroups

本文引入了在黎曼流形上基于形式的横向平均算子，通过横向李代数作用的积分，不依赖全局群作用。主要应用计算了齐性空间G/H的微分拓扑de Rham上同调，证明了其与李代数上同调的同构性。

对称对与分支律

Symmetric pairs and branching laws

本文研究紧李群对称对的分支律，利用复约化子群在旗簇上有限轨道的经典结果，给出由轨道空间 $H_C\ackslash F$ 参数化的分支系数公式。