Moore空间Pn(8)及其同伦群

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).Pn(k)=Sn-1∪kln-1en为型为(Zk,n-1)的Moore空间.特别地,考虑k=8,决定了Moore空间Pn(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Pn(8)到n维球面Sn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π(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∪en.     

(i1i)*(b12k0)及(i1i)*(b31k0)在π*V(1)中的收敛性

对连通有限型谱X,y,存在Adams谱序列{Es,tr,dr},满足(1)dr:Es,t,r→Es+r,t+r-1,r是谱序列的微分, (2)Es,t,2≌Exts,t,A(H*X,H*y),(3)收敛到[∑t-sY,X].当X分别是球谱S,Moore谱M,Toda-smith谱V(1)时,(πt-X)p分别是S,M,V(1)的稳定同伦群.利用Adams 谱序列,证明了(i1i)*(62,1k0)及(i1i)*(b3,1k0)是永久循环但不是边缘,因此收敛到π*V(1)中的非零元,其中P为奇索数,q=2p-2.     

Two New Families in the Stable Homotopy Groups of Sphere and Moore Spectrum

This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree pnq pmq q - 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree pnq pmq q - 3 which are represented by h0(hmbn-1-hnbm-1) and i*(h0hnhm) in the E2-terms of the Adams spectral sequence respectively, where p≥7 is a prime, n≥m 2≥4, q = 2(p - 1).     

球面稳定同伦群中的部分第三周期性元素族

考察了对于素数P≥7,当1≤r＜p-3/2时,环谱Vr(2)的交换性、结合性以及其它一些性质,并且还得出了球面稳定同伦群的部分第三周期性元素族γtpn/r(n≥1,t≥1,1≤r≤2n相似文献   

关于co-H-空间上的映射(Ⅱ)

对于 co-H-空间 X 和 Y,本文对所有 X 到 Y 的 co-H-映射的同伦等价类所成的群[X,Y]~H([X,Y]的子群)的秧进行估值,得到如下结论:当 X 满足一定条件时ρ[X,Y]~H≤(?)β_K(X)β_k(Y)以及当取同纬映象结构时ρ[SX,SY]~H=(?)β_K(X)β_k(Y).另外本文还讨论了 co-H-空间和回路空间上的 F-等价问题,并获得一些结果.     

齐性空间SU(2n)/Sp(n)的H-同伦指数

令p为大于3的素数.在一定维数限制下,通过把齐性空间SU(2n)/Sp(n)分解为若干个同伦可结合,同伦可交换的H-空间的乘积,进而得到了SU(2n)/Sp(n)的p素H-同伦指数的一个上界.     

格点空间上的变分复形及应用

运用非交换微分运算,在格点空间上引入变分复形并用代数拓扑的方法证明它的正合性,最后讨论离散变分复形在离散变分问题逆问题上的应用.     

关于M-PN空间中算子方程Tx=μx+p(μ≥1)的解

在M enger PN空间中研究了一类非线性算子方程T x=μx p(μ≥1)的解,得到了几个新的定理.同时,改进和推广了若干个重要结论.     

超积空间及其性质

引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.     

球面稳定同伦群的(~γ)t(~l)1g0新元素族

首先给出了May谱序列Es1,t,u项的几个结果,然后利用这些结果和关于ExtsP,t(Zp,Zp)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂Pi(i≥0)生成的子代数)得出了乘积~γt~l1g0∈Ext*A,*(Zp,Zp)(3≤t＜p-2)在Adams谱序列的收敛性,其中g0∈Ext2A,pq+2q(Zp,Zp),~l1∈Ext3A,p2q+2pq(Zp,Zp).     

Smash Products for Secondary Homotopy Groups

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered. The second author was partially supported by the Spanish Ministry of Education and Science under MEC-FEDER grants MTM2004-01865 and MTM2004-03629, the postdoctoral fellowship EX2004-0616, and a Juan de la Cierva research contract.     

A Relation in the Stable Homotopy Groups of Spheres

Let p≥7 be an odd prime. Based on the Toda bracket α1βp-11, α1 β1, p, γs,the authors show that the relation α1βp-11h2,0 γs= βp/p-1γs holds. As a result, they can obtain α1βp1h2,0 γs = 0 ∈π*(S0) for 2≤s≤p- 2, even though α1h2,0γs and β1α1h2,0 γs are not trivial. They also prove that βp-11α1 h2,0 γ3 is nontrivial in π*(S0) and conjecture that βp-11α1 h2,0 γs is nontrivial in π*(S0) for 3≤s≤p- 2. Moreover, it is known thatβp/p-1γ3 = 0 ∈ Ext5,*BP*BP(BP*, BP*), but βp/p-1γ3 is nontrivial in π*(S0) and represents the element βp-11α1 h2,0 γ3.     

Gottlieb groups of spheres

This paper takes up the systematic study of the Gottlieb groups of spheres for k≤13 by means of the classical homotopy theory methods. We fully determine the groups for k≤13 except for the 2-primary components in the cases: k=9,n=53;k=11,n=115. In particular, we show if n=2ⁱ−7 for i≥4.     

On the Cohomology of Categories, Universal Toda Brackets and Homotopy Pairs

A category of homotopy pairs is characterised by a cohomology class which generalizes the notion of Toda bracket. Explicit computations of such cohomology classes are described.     

The certain exact sequence of Whitehead and the classification of homotopy types of CW-complexes

This paper defines an invariant associated to Whitehead's certain exact sequence of a simply connected CW-complex which is much more elementary — and less powerful — than the boundary invariant of Baues. Nevertheless, in good cases, it classifies the homotopy types of CW-complexes.     

Fock空间上的对偶Toeplitz代数

通过符号映射研究Fock空间之正交补空间上对偶Toeplitz代数的结构,得到了Fock空间上对偶Toeplitz代数的一个短正合序列.并研究了对偶Toeplitz算子谱的性质.     

Arveson空间中元素的乘积

设f_1,f_2,…,f_d是Arveson空间中的元素,利用Hilbert模的张量积,证明它们的乘积在经典的Hardy空间中。     

(i,p) -同伦逆和群同伦逆

该文在点标拓扑空间范畴中引进了(i,p)-同伦逆和群同伦逆的概念,并讨论了它们存在的条件和性质.