Algebraic & Geometric Topology

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

Linan Zhong and Yuyu Wang

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715698

Digital Object Identifier
doi:10.2140/agt.2013.13.3009

Mathematical Reviews number (MathSciNet)
MR3116311

Zentralblatt MATH identifier
1272.55009

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

Keywords
stable homotopy groups of spheres Adams spectral sequence May spectral sequence

Citation

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. https://projecteuclid.org/euclid.agt/1513715698


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