Volume 10, issue 4 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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 βtp2r 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 βtp2r 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 2000
Primary: 55Q45
Secondary: 55Q10
References
Publication
Received: 21 August 2009
Revised: 26 March 2010
Accepted: 2 September 2010
Published: 16 October 2010
Authors
Katsumi Shimomura
Department of Mathematics
Faculty of Science
Kochi University
2-5-1
Akebono
Kochi 780-8520
Japan