论文标题
减少$ s^3 $ heegaard分裂的属领域
Reducing spheres of genus-2 Heegaard splitting of $S^3$
论文作者
论文摘要
标准属G heegaard的三个球体$ g_g $的Goeritz小组在减少球体的同位素类别的空间上进行了这种Heegaard分裂。 Scharlemann MR2199366（2007C：57020）使用此操作证明$ G_2 $有限地生成。在本文中，我们给出了一种算法来构建从标准降低球体中的任何减少球体，用于$ s^3 $的属-2 Heegaard分裂。使用此功能，我们给出了有限生成$ G_2 $的替代证明，假设标准还原球的稳定器有限生成。
The Goeritz group of the standard genus-g Heegaard splitting of the three sphere, $G_g$, acts on the space of isotopy classes of reducing spheres for this Heegaard splitting. Scharlemann MR2199366 (2007c:57020) uses this action to prove that $G_2$ is finitely generated. In this article, we give an algorithm to construct any reducing sphere from a standard reducing sphere for a genus-2 Heegaard splitting of the $S^3$. Using this we give an alternate proof of the finite generation of $G_2$ assuming the finite generation of the stabilizer of the standard reducing sphere.
