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(pn + sp + 2) 4. These nontrivial homotopy elements are represented by β̃sh0hn in the E2s+2,t–term of the Adams spectral sequence, where p 5, n > 4, p + 1 < s < 2p 1, t = q(pn + sp + 2) + s 2, q = 2(p 1).

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