A nontrivial product of filtration s+5 in the stable homotopy of spheres

作者：Liu Xiu Gui^*

来源：Acta Mathematica Sinica-English Series, 2007, 23(3): 385-392.

DOI：10.1007/s10114-005-0548-y

• stable homotopy of spheres
• Adams spectral sequence
• Toda-Smith spectrum
• May spectral sequence

In this paper, some groups Ext(A)(s,t) (Z(p), Z(p)) with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s + 5 in the stable homotopy groups of spheres pi Spnq+(epsilon+3)pq+(s+1)q-5 which is represented (up to a nonzero scalar) by beta(s+2)b(0)h(n)is an element of Ext(A)(s+5,pnq+(s+3)pq+(s+1)q+s) (Z(p),Z(p)) in the Adams spectral sequence, where p >= 5 is a prime number, n >= 3, 0 <= s < p-3, q = 2(p-1).

• 出版日期2007-3
• 单位南开大学