## Algebraic & Geometric Topology

### Products of Greek letter elements dug up from the third Morava stabilizer algebra

#### Abstract

In [Hiroshima Math. J. 12 (1982) 611–626], Oka and the second author considered the cohomology of the second Morava stabilizer algebra to study nontriviality of the products of beta elements of the stable homotopy groups of spheres. In this paper, we use the cohomology of the third Morava stabilizer algebra to find nontrivial products of Greek letters of the stable homotopy groups of spheres: $α1γt$, $β2γt$, $〈α1,α1,βp∕pp〉γtβ1$ and $〈β1,p,γt〉$ for $t$ with $p∤t(t2−1)$ for a prime number $p>5$.

#### Article information

Source
Algebr. Geom. Topol., Volume 12, Number 2 (2012), 951-961.

Dates
Revised: 29 November 2011
Accepted: 8 January 2012
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715376

Digital Object Identifier
doi:10.2140/agt.2012.12.951

Mathematical Reviews number (MathSciNet)
MR2928900

Zentralblatt MATH identifier
1245.55005

Subjects
Primary: 55Q45: Stable homotopy of spheres
Secondary: 55Q51: $v_n$-periodicity

#### Citation

Kato, Ryo; Shimomura, Katsumi. Products of Greek letter elements dug up from the third Morava stabilizer algebra. Algebr. Geom. Topol. 12 (2012), no. 2, 951--961. doi:10.2140/agt.2012.12.951. https://projecteuclid.org/euclid.agt/1513715376

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