A nontrivial homotopy element of order p ² detected by the classical Adams spectral sequence

Abstract

Let p be an odd prime. The authors detect a nontrivial element ã _p of order p ² in the stable homotopy groups of spheres by the classical Adams spectral sequence. It is represented by $a_0^{p - 2} h_1 \in Ext_A^{p - 1,pq + p - 2} (\mathbb{Z}/p,\mathbb{Z}/p)$ in the E ₂-term of the ASS and meanwhile p · ã ^p is the first periodic element α ^p.

Keywords

Stable homotopy groups of sphere / Adams spectral sequence / May spectral sequence / Massey product

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