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# 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

#### 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