论文标题
浸没功能的拓扑等效性和在飞机上叶子的拓扑等效性：线性案例
Topological equivalence of submersion functions and topological equivalence of their foliations on the plane: the linear-like case
论文作者
论文摘要
令$ f，g：\ mathbb {r}^2 \ to \ mathbb {r} $是两个累积功能，$ \ mathscr {f}（f}（f）$和$ \ mathscr {f}（g）$是$ \ mathbb {r}^2 $的常规for $ ns p $ n compent $ n comment compons的定期。 $ f $和$ g $的拓扑等效性意味着$ \ mathscr {f}（f）（f）$和$ \ mathscr {f}（g）$的拓扑等效性，但总体上不正确。在本文中，我们介绍了类似线性的沉浆函数，该功能足够宽，可以包含非平凡的行为，并提供了相反含义对该类功能的有效性的条件。我们的结果导致我们在某些线性浸没功能的某些子类中拓扑等效的完全拓扑不变。
Let $f, g: \mathbb{R}^2 \to \mathbb{R}$ be two submersion functions and $\mathscr{F}(f)$ and $\mathscr{F}(g)$ be the regular foliations of $\mathbb{R}^2$ whose leaves are the connected components of the levels sets of $f$ and $g$, respectively. The topological equivalence of $f$ and $g$ implies the topological equivalence of $\mathscr{F}(f)$ and $\mathscr{F}(g)$, but the converse is not true, in general. In this paper, we introduce the class of linear-like submersion functions, which is wide enough in order to contain non-trivial behaviors, and provide conditions for the validity of the converse implication for functions inside this class. Our results lead us to a complete topological invariant for topological equivalence in a certain subclass of linear-like submersion functions.
