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

Zhong, Linan; Wang, Yuyu

doi:10.2140/agt.2013.13.3009

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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

DOI: 10.2140/agt.2013.13.3009

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 $q (p^{n} + s p + 2) - 4$ . These nontrivial homotopy elements are represented by ${\tilde{β}}_{s} h_{0} h_{n}$ in the $E_{2}^{s + 2, t}$ –term of the Adams spectral sequence, where $p \geq 5$ , $n > 4$ , $p + 1 < s < 2 p - 1$ , $t = q (p^{n} + s p + 2) + s - 2$ , $q = 2 (p - 1)$ .

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

Volume 13, issue 5 (2013)