The Homotopical Classification Of A Kind Of CW-Complex

In this paper, we further discuss the classification of polyhedron on the basis of reference [20], which is a kind of CW-complex with p-localization, n — 1-connected as well as its dimension is no more than n + i — 1. It is necessary that n is big enough, and i ≤ 4p — 5 for convinence. We have got not only the general method on how to classify the polyhedron A_p,n,4p-5 in theory, but also present the homotopical classification on several CW spaces which are easily computed through them.In Chapter 1, we present some very important basic knowledge on algebraic topology, such as the construction of p-localization on sphere, the p-localization space of simple connected CW -complex, the homotopy group of p-localization Moore space.In Chapter 2, we present some elementary properties of mapping cone. In Chapter 3, we discuss the properties of polyhedron A_p,n,2p-3.In Chapter 4, the polyhedron A_p,n,4p-5, say X, is presented in the form of mapping cone. i.e. X (?) K (?)f CK. In which K and K are both the wedge sum of some p- localization Moorespaces.In Chapter 5, basic polyhedron is introduced in order to present the standard form of polyhedron.In Chapter 6, two correlation matrixes < f > and << f >> of polyhedron X are introduced. The homotopical classification of polyhedron is done by making use of transforming its corresponding matrix to the standard one through eighteen admissible transformation of homotopy type invariant. By the way, the eighteen admissible transformation is indispensable tool and core in the process of transforming polyhedron to standard one.Chapter 7 is special as well as important. In this Chapter, the definition of some: kinds of special CW-complex A_p,n,i^s,t(a.X^il, … ,X^iv) is presented, the element of which is polyhedron A_p,n.i. The homotopical classification of the CW-complex is carried out by using the program made by myself. Every kind of specific representative can also be transformed to standard one by the program if necessary. The main results are presented as follows: A_3,n,3^3,3(0, K⁰, A¹) has thirteen homotopical classes; A_3,n,3^3,3(1, K⁰, A¹) has five homotopical classes; A_3,n,3^3,3(2, K⁰,A¹) also has five homotopical classes; A_3,n,3^2,2(0, K⁰, A¹, K¹) has thirty-nine homotopical classes; and A_3,n,3^2,2(1, K⁰, A¹. K¹) has fifteen homotopical classes.At last, personal program code is presented as an appendix.