Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unstable compositions related to the image of $ J$


Authors: Mark Mahowald and Robert Thompson
Journal: Proc. Amer. Math. Soc. 102 (1988), 431-436
MSC: Primary 55Q40,; Secondary 55Q50
MathSciNet review: 921012
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Abstract: We study elements in the homotopy groups of spheres which are desuspensions of generators of the image of the $ J$-homomorphism for $ p = 2$. $ {J_*}({\mathbf{R}}{P^\infty })$ is used to detect the nontriviality of compositions and Toda brackets involving these elements. Some formulas are derived which show how various compositions of these elements are related to one another.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0921012-X
Keywords: Homotopy groups of spheres, $ J$-homomorphism, Toda brackets, connective $ K$-theory, projective space
Article copyright: © Copyright 1988 American Mathematical Society