Geodesic
Products of Greek letter elements dug up from the third Morava stabilizer algebra
Kato, Ryo1 ; Shimomura, Katsumi2
1Graduate school of Mathematics, Nagoya Unversity, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
2Department of Mathematics, Faculty of Science, Kochi University, 2-5-1, Akebono, Kochi 780-8520, Japan
Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 951-961
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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.

DOI : 10.2140/agt.2012.12.951
Classification : 55Q45, 55Q51
Keywords: BP–theory, stable homotopy of spheres

Kato, Ryo  1   ; Shimomura, Katsumi  2

1 Graduate school of Mathematics, Nagoya Unversity, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
2 Department of Mathematics, Faculty of Science, Kochi University, 2-5-1, Akebono, Kochi 780-8520, Japan 
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Kato, Ryo; Shimomura, Katsumi. Products of Greek letter elements dug up from the third Morava stabilizer algebra. Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 951-961. doi: 10.2140/agt.2012.12.951

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