Smith-Toda谱同伦群中的非平凡元素

A nontrivial element in homotopy group of Smith-Toda spectrum

考虑V(1)谱的同伦群.首先借助May谱序列得到V(2)谱的上同调群的一些结论,然后用代数方法证明了在Adams谱序列中,(b_1)~2g_1∈Ext_A^(6,3p^2q+2pq)(H*V(1),Z_p)是永久循环且不是dr边缘,从而收敛到π_(3p^2q+2pq-6V)(1)中的非零元.

The homotopy group of spectrum V（1） is considered, some conclusions about cohomolopy group of spectrum V（2） are obtained by using May spectral sequences. And then it is proved that （b1）^2g1∈ExtA^6,3p^2q＋2pq（H＊V（1）,Zp） is a permanent cycle and can＇t be hit by any differential in the Adams spectral sequence by using algebra method, this is to say it converges to a notrivial homotopy element in π3p^2q＋2pq-6V（1）.