论文标题
有限的2复合物中同源类别的最小属
The Minimal Genus of Homology Classes in a Finite 2-Complex
论文作者
论文摘要
我们研究有限复合物的同源性类别的表面代表，这些综合体的某些复杂性度量（包括其属和欧拉的特征）最小化。我们的主要结果是，在无效曲线下进行手术最小化器对2个骨骼的细胞覆盖物是同型的。从中，我们得出的结论是，最小化的问题通常在算法上是不可确定的，但可以解决二维CAT（-1） - 复合物。
We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are homotopic to cellwise coverings to the 2-skeleton. From this we conclude that the minimizing problem is in general algorithmically undecidable, but can be solved for 2-dimensional CAT(-1)-complexes.
