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2010 The beta elements $\beta_{tp^2/r}$ in the homotopy of spheres
Katsumi Shimomura
Algebr. Geom. Topol. 10(4): 2079-2090 (2010). 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 βtp2r for positive integers t and r survive to the homotopy of spheres at a prime p>3, when r2p2 and r2p if t>1. In this paper, for p>5, we expand the condition so that βtp2r for t1 and rp22 survives to the stable homotopy groups.

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Katsumi Shimomura. "The beta elements $\beta_{tp^2/r}$ in the homotopy of spheres." Algebr. Geom. Topol. 10 (4) 2079 - 2090, 2010. https://doi.org/10.2140/agt.2010.10.2079

Information

Received: 21 August 2009; Revised: 26 March 2010; Accepted: 2 September 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1223.55007
MathSciNet: MR2745666
Digital Object Identifier: 10.2140/agt.2010.10.2079

Subjects:
Primary: 55Q45
Secondary: 55Q10

Rights: Copyright © 2010 Mathematical Sciences Publishers

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