#### Volume 10, issue 4 (2010)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Other MSP Journals
The beta elements $\beta_{tp^2/r}$ in the homotopy of spheres

### Katsumi Shimomura

Algebraic & Geometric Topology 10 (2010) 2079–2090
##### Abstract

In In [Ann. Math. (2) 106 (1977) 469–516], Miller, Ravenel and Wilson defined generalized beta elements in the ${E}_{2}$–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 ${\beta }_{t{p}^{2}∕r}$ for positive integers $t$ and $r$ survive to the homotopy of spheres at a prime $p>3$, when $r\le 2p-2$ and $r\le 2p$ if $t>1$. In this paper, for $p>5$, we expand the condition so that ${\beta }_{t{p}^{2}∕r}$ for $t\ge 1$ and $r\le {p}^{2}-2$ survives to the stable homotopy groups.

##### Keywords
homotopy of spheres, beta family, Adams–Novikov spectral sequence
Primary: 55Q45
Secondary: 55Q10