Unstable compositions related to the image of

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 -homomorphism for . 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.

**[A]**J. F. Adams,*On the groups 𝐽(𝑋). IV*, Topology**5**(1966), 21–71. MR**0198470****[DM]**Donald M. Davis and Mark Mahowald,*𝑣₁- and 𝑣₂-periodicity in stable homotopy theory*, Amer. J. Math.**103**(1981), no. 4, 615–659. MR**623131**, 10.2307/2374044**[M1]**Mark Mahowald,*The image of 𝐽 in the 𝐸𝐻𝑃 sequence*, Ann. of Math. (2)**116**(1982), no. 1, 65–112. MR**662118**, 10.2307/2007048**[M2]**-,*Descriptive homotopy of the elements in the image of the**-homomorphism*, Proc. Tokyo Conf. Manifolds, 1973, pp. 255-263.**[S]**V. P. Snaith,*A stable decomposition of Ωⁿ𝑆ⁿ𝑋*, J. London Math. Soc. (2)**7**(1974), 577–583. MR**0339155**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1988-0921012-X

Keywords:
Homotopy groups of spheres,
-homomorphism,
Toda brackets,
connective -theory,
projective space

Article copyright:
© Copyright 1988
American Mathematical Society