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
Publication
Received: 28 September 2011
Revised: 27 September 2012
Accepted: 30 September 2012
Published: 31 July 2013
Authors
 Linan Zhong Department of Mathematics Yanbian University No. 977, Gong Yuan Road Yanji 133000 China and School of Mathematical Sciences Nankai University Tianjin 300071 China Yuyu Wang College of Mathematical Science Tianjin Normal University No.393, Extension of Bin Shui West Road, Xi Qing District Tianjin 300387 China