文档介绍：摘要球面稳定同伦群的计算是代数拓扑中同伦论的中心问题, PSteenrod代数(p为素数),S为P局部化的球谱.∥为A的对偶,尸表示A的由循环缩减幂Pi(i≥o) 谱序列(Ass):露乒=E疵岔(名,乙)令丌t一。S,其中露≯是A的上同调;May谱序列(Mss)[9]=当p>2时,存在研^4号E疵警(乙,名),使得E1气屯‘=E(hi,J i>0,歹≥0)oP(玩,j i>0,J≥0)o P(aii≥o),其中E表示外代数,P表示多项式代数,而且%,,∈磅,2(pi-1)矿,2扣1,玩,,∈。E】2,2(p‘--1)p/+l,p(2i--1),ai∈E;,2pi--1,2i+1. 在第一章中利用Adams谱序列,证明了(ili)。(6;梳)及(t,t)。(堵‰)是永久循环但不是边缘,因此收敛到7r+y(1) 谱序列,证明了(i2i1{)。(61f1)是永久循环但不是边缘,因此收敛到7r。v(2) ,运用TMay谱序歹U(MSS),得到-J"Ext群一些非平凡或平凡乘积的结果. 关键词:Adams谱序列,Toda谱y(佗),正合序列,Ext群,May谱序列, 稳定同伦群 Abstract Todetermine the stable homotopy groups ofsphere丌。S isthe central and difficultproblems inhomotopy theory inalgebraic A bethemod P Steenrod algebra and Sthe sphere spectrum localized at an odd prime A。be the duality ofA and P be the subal— gebra ofA generated by reduced powers P(i≥0).We have the clas- sicalAdams spectralsequence(ASS):霹#=E耐岔(乙,乙)号矶一8S, where E;'t-term isthecohomology most essful method puting the Ext groups istheMay spectral sequence(MSS)[9]:For P>2,there exits曰^。兮E疵警(名,乙)such that日产一=E(hi,J i>0,歹≥0)o P(bi,ji>0,J≥0)圆P(ai i≥o),where E isthe exterior algebra,P isthepolynomial algebra,and ht,J∈研’2∽一1)矿’2¨, bi,J∈,2(pi--1)p/+l,p(2i-1),ot∈砖2p‘一1,2州. In chapter one,bY using Adams spectr 6tL sequence,it proves that (ili)。(6iko)and(ili)。(b{ko)are both permanent cirlesbut not edges,and converge to an nontrivial elements of7r}y(1).Where P isodd prime =2p一2. Inchapter two,it proves that(i2ili)$(bill)converges to an nontrivial ele- mentof丌。y(2).Then inchapter three,we determine some trivial or non— trivialresults ofExt groups by using theMay spectral sequence(MSS). Keywords:Adams spectr al—sequence,Toda spectrum y(n),exact se- quence,Ext group,May spectr ,The stablehomotopy group II 南开大学学位论文版权使用授权书本人完全了解南开大学关于收集、保存、使用学位论文的规定, 同意如下各项内容:按照学校要求提交学位论文的印刷本和电子版本;学校有权保存学位论文的印刷本和电子版,并采用影印、缩印、扫描、数字化或其它手段保存论文;学校有权提供目录检索以及提供本学位论文全文或者部分的阅览服务;学校有权按有关规定向国家有关部门或