#### Volume 13, issue 5 (2013)

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Detection of a nontrivial product in the stable homotopy groups of spheres

### Linan Zhong and Yuyu Wang

Algebraic & Geometric Topology 13 (2013) 3009–3029
##### Abstract

In this paper, we prove that there exists a new family of nontrivial homotopy elements in the stable homotopy groups of spheres with dimension $q\left({p}^{n}+sp+2\right)-4$. These nontrivial homotopy elements are represented by ${\stackrel{̃}{\beta }}_{s}{h}_{0}{h}_{n}$ in the ${E}_{2}^{s+2,t}$–term of the Adams spectral sequence, where $p\ge 5$, $n>4$, $p+1, $t=q\left({p}^{n}+sp+2\right)+s-2$, $q=2\left(p-1\right)$.

##### Keywords
stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence
##### Mathematical Subject Classification 2010
Primary: 55Q45
Secondary: 55T15, 55S10