中文摘要：

令G是一Abel群,m≥2是一整数．一个型为（G,m）的Moore空间是一单连通的CW-复形X,使得Hi（X）=G（i=m）,0（i≠m）．这里Hi为X的第i个整系数的约化同调群．众所周知,Moore空间存在,且任何两个型为（G,n）的Moore空间有相同伦型．取G=Zk（模k的剩余类加群）．p^n（k）=S^n-1∪kln-1e^n为型为（Zk,n-1）的Moore空间．特别地,考虑k=8,决定了Moore空间p^n（8）的一些同伦群．主要证明工具是Toda引进的复合工具-Toda积,Gray的关于从p^n（8）到n维球面S~n的pinchin映射的同伦纤维的胞腔结构,以及关于亚稳定相对同伦群πk（X,A）的同伦切割定理,其中A为维数小于n-1的有限CW-复形,X=A∪e^n．

英文摘要：

Let G be an Abelian group and m an integer m ≥ 2. A Moore space of type （G,m） is a 1-connected CW-complex X such that H^-i（X） = G for i = m, and 0 for others. HereH^-i denotes the i-th reduced homology groups. It is well known that Moore spaces exist and that any two of type （G, n） have the same homotopy type. This paper fixes G = Zk, the integers mod k and let P^n（k） = S^n-1 Ukln-1 e^n be a Moore space of type （Zk,n - 1）. In particular, the author considers the case k = 8 and calculate some homotopy groups of the Moore space P^n（8）. The methods are based upon the composition methods developed by Toda. And uses Gray＇s cellar structure of the homotopy fibre of the pinching map from P^n（8） to an n-sphere S^n and also uses the homotopy excision theorem about the metastable relative homotopy groups πk （X, A）, where A is a finite CW-complex of dimension less than n-1 andX=A∪e^n.