论文标题
普通社区的叶面和紧凑的同位素
Foliated and compactly supported isotopies of regular neighborhoods
论文作者
论文摘要
令$ \ Mathcal {f} $为平滑的歧管$ m $和$ p：e \ to b $的“单数” submanifold $ b $的叶面，为$ m $中的$ b $的常规社区。在某些“同质性”假设下，对$ \ MATHCAL {f} $接近$ b $，我们证明，每个保留叶子的差异性$ h $ of $ m $ a $ m $都是同位素，这是同位素的同位素，通过保留叶子的同位素，与差异$ e $ e $ $ b $相吻合。该结果是一个互惠互为支持的变体的一个众所周知的变体，即$ \ mathbb {r}^n $固定的每个差异性$ h $ of $ \ mathbb {r}^n $ firmit对线性同位素是由$ 0 $ 0 $ 0 $ h $ $ h $的线性同构的同位素。我们还向$ \ Mathcal {f} $的叶片保存差异的同型类型的计算提供了应用。
Let $\mathcal{F}$ be a foliation with a "singular" submanifold $B$ on a smooth manifold $M$ and $p:E \to B$ be a regular neighborhood of $B$ in $M$. Under certain "homogeneity" assumptions on $\mathcal{F}$ near $B$ we prove that every leaf preserving diffeomorphism $h$ of $M$ is isotopic via a leaf preserving isotopy to a diffeomorphism which coincides with some vector bundle morphism of $E$ near $B$. This result is mutually a foliated and compactly supported variant of a well known statement that every diffeomorphism $h$ of $\mathbb{R}^n$ fixing the origin is isotopic to the linear isomorphism induced by its Jacobi matrix of $h$ at $0$. We also present applications to the computations of the homotopy type of the group of leaf preserving diffeomorphisms of $\mathcal{F}$.
