Homology, Homotopy and Applications

Volume 10 (2008)

Number 3

Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson

An algebraic generalization of image $J$

Pages: 321 – 333

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n3.a14

Author

Hirofumi Nakai (Department of Mathematics, Musashi Institute of Technology, Tokyo, Japan)

Abstract

As is well known, the image of the $J$-homomorphism in the stable homotopy groups of spheres is described in terms of the first line of the Adams-Novikov $E_2$-term. In this paper we consider an algebraic analogue of the image of $J$ using the spectrum $T(m)_(j)$ defined by Ravenel and determine the Adams-Novikov first line for small values of $j$.

Keywords

stable homotopy of spheres; Adams-Novikov spectral sequence

2010 Mathematics Subject Classification

55Q45

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