A new family in the stable homotopy groups of spheres

Document Type: Research Paper


1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R China

2 Mathematics and Information Science College,Hebei Normal University, 050016,Shijiazhuang, P. R. China


Let $p$ be a prime number greater than three. In this paper, we
prove the existence of a new family of homotopy elements in the
stable homotopy groups of spheres $pi_{ast}(S)$ which is
represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4,
q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero
scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq
Ext}_A^{s+2,q[(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ was
defined by X. Wang and Q. Zheng.