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 sph...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.展开更多
This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq...This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq ＋ p^mq ＋ q - 3 which are represented by h0（hmbn-1 - hnbm-1） and ie（hohnhm） in the E2-terms of the Adams spectral sequence respectively, where p ≥ 7 is a prime, n ≥ m ＋ 2 ≥ 4, q = 2（p - 1）.展开更多
文摘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Project supported by the National Natural Science Foundation of China (No.10171049)
文摘This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq ＋ p^mq ＋ q - 3 which are represented by h0（hmbn-1 - hnbm-1） and ie（hohnhm） in the E2-terms of the Adams spectral sequence respectively, where p ≥ 7 is a prime, n ≥ m ＋ 2 ≥ 4, q = 2（p - 1）.
