- Turkish Journal of Mathematics
- Vol: 35 Issue: 2
- Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequ...
Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequence
Authors : Xiugui Liu
Pages : 311-321
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E2-term of the Adams spectral sequence, ExtA\ast,\ast (Zp,Zp). In this paper we prove that in the cohomology of A, the product k0 hn \tilde d s + 4 \in ExtAs + 7, t(s,n) + s (Zp, Zp), is nontrivial for n \geq 5, and trivial for n=3, 4, where \tildeds + 4 is actually \tildeas + 4(4) described by Wang and Zheng, p \geq 11, 0 \leq s < p - 4 and t(s,n)=2(p-1)[(s + 2) + (s + 4)p + (s + 3)p2 + (s + 4)p3 + pn].Keywords : Key words: Steenrod algebra, cohomology, Adams spectral sequence, May spectral sequence