Algebraic & Geometric Topology

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

Linan Zhong and Yuyu Wang

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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 p5, n>4, p+1<s<2p1, t=q(pn+sp+2)+s2, q=2(p1).

Article information

Algebr. Geom. Topol., Volume 13, Number 5 (2013), 3009-3029.

Received: 28 September 2011
Revised: 27 September 2012
Accepted: 30 September 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55Q45: Stable homotopy of spheres
Secondary: 55T15: Adams spectral sequences 55S10: Steenrod algebra

stable homotopy groups of spheres Adams spectral sequence May spectral sequence


Zhong, Linan; Wang, Yuyu. Detection of a nontrivial product in the stable homotopy groups of spheres. Algebr. Geom. Topol. 13 (2013), no. 5, 3009--3029. doi:10.2140/agt.2013.13.3009.

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