摘要
This study proves a general result on convergence of α2x ∈ ExtA^s+2.tq+2q+1 (Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq+2q+1(Zp,Zp) with tq=p^n+1q+2p^nq,2p^n+1q_P^nq,p^uq+p^mq+p^nq,respectively, where α2∈Extα^2,2q+1(Zp,Zp),fn∈ExtA^3,p^n+1q+2p^nq(Zp,Zp),fn∈ExtA^3,2p^n+2q+p^nq(Zp,Zp),hn∈ExtA^1,p^nq(Zp,Zp)and p≥5 is a prime,q=2(p=-1),n≥2.
This study proves a general result on convergence of α2x ∈ ExtA^s+2.tq+2q+1 (Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq+2q+1(Zp,Zp) with tq=p^n+1q+2p^nq,2p^n+1q_P^nq,p^uq+p^mq+p^nq,respectively, where α2∈Extα^2,2q+1(Zp,Zp),fn∈ExtA^3,p^n+1q+2p^nq(Zp,Zp),fn∈ExtA^3,2p^n+2q+p^nq(Zp,Zp),hn∈ExtA^1,p^nq(Zp,Zp)and p≥5 is a prime,q=2(p=-1),n≥2.
基金
Supported by NSFC (10171049)