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

Kato, Ryo; Shimomura, Katsumi

doi:10.2140/agt.2012.12.951

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

Ryo Kato and Katsumi Shimomura

Algebraic & Geometric Topology 12 (2012) 951–961

DOI: 10.2140/agt.2012.12.951

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: $α_{1} γ_{t}$ , $β_{2} γ_{t}$ , $〈 α_{1}, α_{1}, β_{p ∕ p}^{p} 〉 γ_{t} β_{1}$ and $〈 β_{1}, p, γ_{t} 〉$ for $t$ with $p ∤ t (t^{2} - 1)$ for a prime number $p > 5$ .

Keywords

BP–theory, stable homotopy of spheres

Mathematical Subject Classification 2010

Primary: 55Q45

Secondary: 55Q51

References

Publication

Received: 1 August 2011

Revised: 29 November 2011

Accepted: 8 January 2012

Published: 24 April 2012

Authors

Ryo Kato
Graduate school of Mathematics Nagoya Unversity Furo-cho, Chikusa-ku Nagoya 464-8602 Japan

Katsumi Shimomura
Department of Mathematics, Faculty of Science Kochi University 2-5-1, Akebono Kochi 780-8520 Japan

Volume 12, issue 2 (2012)