论文标题
紧凑的4个manifolds的结晶最小化组合定义的PL不变性
Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants
论文作者
论文摘要
The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL $4$-manifolds with empty or connected boundary, called {\it semi-simple} and {\it weak semi-simple crystallizations}, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the {\it regular genus}, the {\ it gurau deger}，{\ it gem-complexity}和{\ it（gem诱导的）trisection gen}。主要定理对该主题产生了总结结果，是原始贡献。此外，在本文中，事实证明，常规属相对于连接总和的添加性可容纳所有紧凑型$ 4 $ - 具有空的或连接的边界的$ 4 $ manifolds，从而允许弱的半简单结晶。
The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL $4$-manifolds with empty or connected boundary, called {\it semi-simple} and {\it weak semi-simple crystallizations}, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the {\it regular genus}, the {\it Gurau degree}, the {\it gem-complexity} and the {\it (gem-induced) trisection genus}. The main theorem, yielding a summarizing result on the topic, is an original contribution. Moreover, in the present paper the additivity of regular genus with respect to connected sum is proved to hold for all compact $4$-manifolds with empty or connected boundary which admit weak semi-simple crystallizations.
