| 白建侠.(i1i)*(b12k0)及(i1i)*(b31k0)在π*V(1)中的收敛性[J].数学年刊A辑,2009,30(3):377~390 |
| (i1i)*(b12k0)及(i1i)*(b31k0)在π*V(1)中的收敛性 |
| The Convergence of (i1i),(b2,1k0) and (i1i).(b3,1k0) |
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| DOI： |
| 中文关键词: Adams谱序列 Toda谱V(n) 正合序列 Ext群 |
| 英文关键词:Adams spectrum sequence, Toda spectrum V (n), Exact sequence,
Ext group |
| 基金项目:国家自然科学基金(No.10171049)资助的项目 |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| For connected finite type spectra $X$, $Y$, there
exists Adams spectral
space $\{E_r^{s,t},d_r\}$, such that
(1) $d_r:E_r^{s,t}\rightarrow{E_r^{s+r,t+r-1}}$ is the
differential,
(2) $E_2^{s,t}\cong {\rm Ext}^{s,t}_A(H^*X,H^*Y)$,
(3) it converges to $[\sum^{t-s}Y,X].$\when $X$ is sphere spectrum $S$, Moore spectrum $M$, Toda-smith
spectrum $V(1)$, $(\pi_{t-s}X)_P$ is respectively the stable homotopy
group of $ S,M,V(1)$. In this paper, by using Adams spectrum sequence,
it is proved that $(i_1i)_*(b_{1}^{2}k_{0})$ and
$(i_1i)_*(b_{1}^{3}k_{0})$ are both permanent circles but not edges,
and converge to annontrivial elements of $\pi_*V(1)$, where $p$ is
odd prime number, $q=2p-2$. |
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