两类合成空间图补空间中的基本曲面

Elementary Surfaces in Two Classes of Composite Spatial Graph Complements

基于合成空间图的定义及基本曲面的性质,利用三维流形组合拓扑的方法,证明了两类合成空间图补空间中具有任意子午线边界分支的基本曲面都是穿孔球面.

Based on the definition of composite spatial graph and the properties of elementary surfaces in the complements of spatial graph, using the combinational methods of 3-manifold, we prove that if the elementary surfaces with meridian boundaries in the complements of the factor graphs are punctured sphere,then the elementary surfaces with meridian boundaries in two classes of composite spatial graph complements are punctured spheres.