The IPI Surfaces In Simple Composite Spatial Graph Complements

In the spatial graph complements,IPI surface properties and classification have always been a hot topic among the scholars who study the 3-manifold topology.A large number of scholars had studied deeply and carefully of the determination methods and properties of incompressible surfaces and IPI surfaces in the range of alternating graph complements.Because of the composite spatial graph is an important part of spatial graph.In order to prove the properties of IPI surfaces in spatial graph complements,this thesis use the properties of IPI surfaces in alternating graph complements extend to the spatial graph complements.This thesis based on definitions of 0-and 1-composite spatial graphs and the properties of IPI surfaces,using the combinatorial methods of 3-manifold to prove that the IPI surfaces with meridian boundaries in the spatial graph complements are punctured spheres.This thesis contains four parts as follows:The first part is the preliminary knowledge of 3-manifolds and its related properties,such as embedded,prime manifolds,regular neighborhood,etc.The related definitions of knots and links;The related definitions of composite spatial graph,alternating spatial graph,incompressible surfaces and IPI surfaces.The second part is about the related properties of the IPI surfaces in links and spatial graph complements.The third part is mainly conclusions of thesis,it prove that if the corresponding decomposition of 0-and 1-composite spatial graph complements have IPI surfaces with meridian boundaries is punctured sphere,then the IPI surfaces with meridian boundaries in the spatial graph complements are punctured spheres.The last part of thesis is the conclusion and prospect.