论文标题
由开放式书籍分解引起的Heegaard分裂的Goeritz组的子组，该分解由保存绑定的元素组成
The subgroup of the Goeritz group of the Heegaard splitting induced by an openbook decomposition consisting of elements preserving the binding
论文作者
论文摘要
当一个3个manifold承认开放式书籍分解时，我们通过增厚的页面来获得Heegaard分裂。这种分裂表面具有来自结合的特殊多曲线。在本文中，我们考虑了此Heegaard拆分的Goeritz组的子组，这是保留给定的Heegaard分裂的3个manifold的映射类组，由保留绑定的元素组成。事实证明，该亚组是保留映射类组的亚组的商，由dehn Twists沿边界曲线产生的亚组的元素组成。我们还获得了Goeritz组元素的存在的标准，该元素将绑定固定为集合并逆转方向。最后，我们给出了一个goeritz组计算的示例。
When a 3-manifold admits an openbook decomposition, we get a Heegaard splitting by thickening a page. This splitting surface has a special multi curves coming from the binding. In this paper, we consider the subgroup of the Goeritz group of this Heegaard splitting, which is the mapping class group of the 3-manifold preserving the given Heegaard splitting, consisting of elements preserving the binding. This subgroup turned out to be the quotient of the subgroup of the orientation preserving mapping class group consisting of elements commuting with the monodromy by the subgroup generated by the Dehn twists along the boundary curves. We also get a criterion for the existence of an element of the Goeritz group which fixes the binding as a set and reverses the orientation. At last, we give some example of computation of a Goeritz group.
