论文标题
在开放式书籍上，嵌入光滑和接触歧管
On open books and embedding of smooth and contact manifolds
论文作者
论文摘要
我们讨论了在开放书籍类别，联系歧管和联系开放书籍类别中的歧管嵌入。我们证明了Haefliger- Hirsch嵌入定理的开放式版本，表明每个$ k $连接的封闭$ n $ -n $ manifold（$ n \ geq 7 $，$ k <\ frac {n-4} {2} {2} $然后，我们证明，每个关闭的歧管$ m^{2n + 1} $，它范围限制了Achiral Lefschetz纤维化，在$ \ Mathbb {s}^{2 \ lfloor \ lfloor \ frac {3n} {3n} {2} {2} {2} {2} {2} {2} {2} {2} {2} {2} {2} \ rfloor + 3} $的$ \ mathbb {s}^{2 \ lfloor \ frac {2 \ lfloor \ rfloor + 3} $中的开放书籍中接受开放式书籍。我们还证明，每个封闭的流形$ m^{2n+1} $界定了一个Achiral Lefschetz纤维纤维，该接触结构承认了一个嵌入在标准接触结构中的触点结构，$ \ m athbb {r}^{2n+3}。最后，我们给出了$（2n的范围$ 1）的各种示例$（2n $ \ mathbb {s}^{4n+1}上的联系结构。$
We discuss embedding of manifolds in the category of open books, contact manifolds and contact open books. We prove an open book version of the Haefliger--Hirsch embedding theorem by showing that every $k$-connected closed $n$-manifold ($n\geq 7$, $k < \frac{n-4}{2}$) admits an open book embedding in the trivial open book of $\mathbb{S}^{2n-k}$. We then prove that every closed manifold $M^{2n+1}$ that bounds an achiral Lefschetz fibration, admits open book embedding in the trivial open book of $\mathbb{S}^{2\lfloor\frac{3n}{2}\rfloor + 3}$. We also prove that every closed manifold $M^{2n+1}$ bounding an achiral Lefschetz fibration admits a contact structure that isocontact embeds in the standard contact structure on $\mathbb{R}^{2n+3}.$ Finally, we give various examples of contact open book embeddings of contact $(2n+1)$-manifolds in the trivial supporting open book of the standard contact structure on $\mathbb{S}^{4n+1}.$
