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Uniqueness of Massey Products on the Stable Homotopy of Spheres

Published online by Cambridge University Press:  20 November 2018

Stanley O. Kochman
Stanley O. Kochman*
Affiliation:
The University of Western Ontario, London, Ontario
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The product on the stable homotopy ring of spheres π*scan be defined by composing, smashing or joining maps. Each of these three points of view is used in Section 2 to define Massey products on π*s. In fact we define composition and smash Massey products (x1, … , xt)where X1, … ,xt-1∈ π*s, xt∈ π*(E) and E is a spectrum. In Theorem 3.2, we prove that these three types of Massey products are equal. Consequently, a theorem which is easy to prove for one of these Massey products is also valid for the other two. For example, [3, Theorem 8.1] which relates algebraic Massey products in the Adams spectral sequence to Massey smash products in π*s is now also valid for Massey composition products in π*s

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 3 , 01 June 1980 , pp. 576 - 589
Copyright
Copyright © Canadian Mathematical Society 2012

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