Algebraic & Geometric Topology 10 (2010) 2079–2090

DOI: 10.2140/agt.2010.10.2079

Abstract

In In [Ann. Math. (2) 106 (1977) 469–516], Miller, Ravenel and Wilson defined generalized beta elements in the E₂–term of the Adams–Novikov spectral sequence converging to the stable homotopy groups of spheres, and in [Hiroshima Math. J. 7 (1977) 427–447], Oka showed that the beta elements of the form β_{tp2 ∕ r} for positive integers t and r survive to the homotopy of spheres at a prime p > 3, when r ≤ 2p − 2 and r ≤ 2p if t > 1. In this paper, for p > 5, we expand the condition so that β_{tp2 ∕ r} for t ≥ 1 and r ≤ p² − 2 survives to the stable homotopy groups.

Keywords

homotopy of spheres, beta family, Adams–Novikov spectral sequence

Mathematical Subject Classification

Primary: 55Q45

Secondary: 55Q10

References

Publication

Received: 21 August 2009
Revised: 26 March 2010
Accepted: 2 September 2010
Published: 16 October 2010

Authors