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 special handle 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 invariants regular genus, gem-complexity or G-degree among all such manifolds with the same second Betti number.

在本文中，我们研究具有空或连接边界的致密PL 4流形的有色三角剖分，这些三角形导致在1个手柄或1个和3个手柄中缺乏手柄分解，因此也面临Kirby所存在的问题。任何简单连接的封闭式PL 4流形的特殊手柄分解。特别是，我们检测到一类具有空的或相连的边界的紧致简单连接的PL 4流形，它允许这种分解，因此可以用（未分配）框架链接表示。此外，此类包括任何紧凑的简单连接的PL 4流形，具有空的或连接的边界，带有彩色三角剖分，可最小化组合定义的PL不变量常规属，宝石复杂度或G度 在所有具有相同第二贝蒂数的歧管中。