Volume 12, issue 2 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
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,βpppγtβ1 and β1,p,γt for t with pt(t2 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