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

2012/02/12 by Ryo Kato, Kato, Ryo, Katsumi Shimomura +1 · 1 citation
Mathematics · #55Q45 #55Q51 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55Q45 #msc:55Q51

paper · pdf · doi:10.48550/arxiv.1202.2519

11 pages

arxiv created 2012/02/12 · arxiv updated 2012/02/14

Abstract

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: \al₁\ga_t, \be₂\ga_t, \lrk\al₁,\al₁,\be_p/p^p\ga_t\be₁ and \lrk\be₁,p,\ga_t for t with p\nmid t(t²-1) for a prime number p>5.

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• A note on the Greek letter elements of the homotopy of the L_n-local spheres

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