论文标题
多型表面的最大和最小属
The maximum and minimum genus of a multibranched surface
论文作者
论文摘要
在本文中，我们给出了一个多数式表面的最大和最小属的下限，分别是第一个betti数和其邻域边界的最小和最大属。作为其应用，我们表明，$ g \ times s^1 $的最大和最小属分别等于图$ g $的最大和最小属的两倍。这提供了图理论与3个模型理论之间的相互作用。
In this paper, we give a lower bound for the maximum and minimum genus of a multibranched surface by the first Betti number and the minimum and maximum genus of the boundary of the neighborhood of it, respectively. As its application, we show that the maximum and minimum genus of $G\times S^1$ is equal to twice of the maximum and minimum genus of $G$ for a graph $G$, respectively. This provides an interplay between graph theory and 3-manifold theory.
