论文标题
紧凑的4个manifolds承认特殊手柄分解
Compact 4-manifolds admitting special handle decompositions
论文作者
论文摘要
在本文中，我们研究了带有空或连接边界的紧凑型PL 4个manifords的彩色三角剖分，这些界限诱发了1个手柄或1个手柄中缺少的手柄分解，因此，柯比（Kirby）也面临着这个问题，存在{\ \ f intercontovers}的存在，因为它是任何简单的封闭pl pl 4- manifords}。特别是，我们检测到具有空或连接边界的一类简单相互连接的PL 4个manifolds，它们接纳了这种分解，因此可以用（未插入的）框架链路表示。此外，此类包括任何具有彩色三角形的简单相互连接的PL 4 manifold，具有彩色三角形的边界，可将组合定义的PL不变{\ em常规属，gem-complexity}或{\ em g-Degree}在所有此类第二BETTTI中的歧管中。
In this paper we study colored triangulations of compact PL 4-manifolds with empty or connected boundary which induce handle decompositions lacking in 1-handles or in 1- and 3-handles, thus facing also the problem, posed by Kirby, of the existence of {\it special handlebody decompositions} for any simply-connected closed PL 4-manifold. In particular, we detect a class of compact simply-connected PL 4-manifolds with empty or connected boundary, which admit such decompositions and, therefore, can be represented by (undotted) framed links. Moreover, this class includes any compact simply-connected PL 4-manifold with empty or connected boundary having colored triangulations that minimize the combinatorially defined PL invariant {\em regular genus, gem-complexity} or {\em G-degree} among all such manifolds with the same second Betti number.
