论文标题
$ c^\ infty $ -Manifolds与骨骼差异学
$C^\infty$-manifolds with skeletal diffeology
论文作者
论文摘要
我们制定和研究$ d $ - 骨骼差异的概念，该概述概括了电线差异学的概念，引入了$ d $ coskeletal diffeology的双重概念。我们首先表明，paracompact有限维$ c^\ infty $ -manifolds $ m_d $带有$ d $ - 骨骼差异学继承了良好的拓扑和$ m $的光滑paracrocactness。然后，我们研究$ M_D $的病理学。最重要的是，我们证明了以下内容：对于$ d <{\ rm dim} \ m $，每个沉浸式$ f：m \ longrightArrow n $在差异空间$ \ dcal（m_d，n_d，n_d，n_d）$ smotive Maps中隔离，$ d $ d $ d $ d $ - 约束的平滑同型$ m_d $是不可能的。
We formulate and study the notion of $d$-skeletal diffeology, which generalizes that of wire diffeology, introducing the dual notion of $d$-coskeletal diffeology. We first show that paracompact finite-dimensional $C^\infty$-manifolds $M_d$ with $d$-skeletal diffeology inherit good topologies and smooth paracompactness from $M$. We then study the pathology of $M_d$. Above all, we prove the following: For $d<{\rm dim}\ M$, every immersion $f:M\longrightarrow N$ is isolated in the diffeological space $\dcal(M_d, N_d)$ of smooth maps and the $d$-dimensional smooth homotopy group of $M_d$ is uncountable.
