Title: A NEW FAMILY ELEMENTS IN THE STABLE HOMOTOPY GROUP OF SPHERES AND THE CONVERGENCE OF h_0~2_1 IN π_*V(1)
Abstract:For connected finite type spectra X, Y. there exists Adams spectral sequence (ASS) (Exr,t,dr) such that (1) dr : Es,tr→Es+r,t+r-1 r is the differential, (2)Es,t2≌Exts,tA(H*(X),H*(Y)), (3) converges to...For connected finite type spectra X, Y. there exists Adams spectral sequence (ASS) (Exr,t,dr) such that (1) dr : Es,tr→Es+r,t+r-1 r is the differential, (2)Es,t2≌Exts,tA(H*(X),H*(Y)), (3) converges to [∑t-sY,X]p. When X is sphere spectrum S, Moore spectum M, Toda-Smith spectrum V(1) respectively, (πt-sX)p is respectively the stable homotopy group of S, M, V(1). This paper detects a new family nonzero elements γth0b21 of the stable homotopy groups of sphere and a nonzero element h0b21 of Toda-Smith spectrum V(1) by using of the ASS. The authors need some results on Ext group by using of the Ext group exact sequences induced by cofibrations of spectrum and by using of May spectral sequence. In this paper, p≥7, which is an odd prime number, and q =2p-1.Read More
Publication Year: 2005
Publication Date: 2005-01-01
Language: en
Type: article
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