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A nontrivial product in the stable homotopy groups of spheres

Authors:	Email author" target="_blank">Xiugui?Liu Email author

Institution:	Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China

Abstract:	Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Liulevicius described h _i and b _k in Ext_A’(Z_p,Z_p) having bigrading (1, sui— 1) and (2, 2p ^k+1 x(p— 1)), respectively. In this paper we prove that for p ≥ 7, n ≥ 4 and $3 \leqslant s < p - 1, h_0 b_{n - 1} \tilde \gamma _s \in Ext_A^{s + 3,p^n q + sp^2 q + (s - 1)pq + (s - 1)q + s - 3} (Z_p ,Z_p )$ survives to E∞ in the Adams spectral sequence, where q = 2(p — 1).

Keywords:	stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectra May spectral sequence
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