Graphlike Manifold With Contraction (?) And (?)

The discovery of manifold is a major advance in modern mathematics .In 1974 ,I. W. morgan and D. P. sullivan demonstrated the concept of Z/n manifold . In 1994 , Liu Yaxing and Li Qisheng demonstrated the concept of a graphlike manifold and researched related topics . Prom then on , more and more algebraic topologists become interested in the field , and have obtained a sequence of important achievements .The n-dimensional framework of (n-1)-dimensional simplex can be transformedinto a vertex undirected graph of n-vertex , called the contraction of graphlike manifold . If we designate the contraction of graphlike manifold ,bockstein (knot or circular) of graphlike manifold can form different graphlike manifold by using different covering map . Calculating all the numbersof homeomorphic classes of graphlike manifold , and providing all kinds of representative elements of graphlike manifolds , are called homeomorphic classification of graphlike manifolds .There are many research methods of graphlike manifold homeomorphism classification , and they are mainly as follows :â… . twist operation ;â…¡. adjoint matrix ;â…¢. combinatorial theory ;â…£. machine computation ;â…¤. combination method .The author of this paper by reading the related to domcuments has researched on the homemorphism class of graphlike manifold with contraction(?)and (?) by reading some related domcuments . and has found out the following points :â… . For outer sides , through twist operation , the negative side of the intersection can always be transformed into non-crossing situation . Thus , we only require to consider non-crossing outer negative sides.â…¡. For inner sides , when the number of inner negative edges is odd , and we do it by twist operation , there only is one negative edge in inner sides . When the number of inner negative edges is even , by twist operation , all the edges are positive in inner sides . Thus , we should only consider two cases : there is only one negative edge or non-negative edge in inner side . Thus , we can simplify the process of calculation .This thesis contains three chapters . The first chapters is to prepare for the proof of the main results of the paper , and introduces the basic concepts and results of graphlike manifold . In addition , this chapter also give out a brief introduction of homeomorphism , topological space , manifold . The second chapter gives a detailed process of calculation and proof of Theory A . The third chapter gives a detailed process of calculation and proof of Theory B .