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2011 On R L Cohen's $\zeta$–element
Xiugui Liu
Algebr. Geom. Topol. 11(3): 1709-1735 (2011). DOI: 10.2140/agt.2011.11.1709

Abstract

Let p be a prime greater than three. In the p–local stable homotopy groups of spheres, R L Cohen constructed the infinite ζ–element ζn1π2pn+12pn+2p5(S) of order p. In the stable homotopy group π2pn+12pn+2p23(V(1)) of the Smith–Toda spectrum V(1), X Liu constructed an essential element ϖk for k3. Let βs=j0j1βs[V(1),S]2sp22s2p denote the Spanier–Whitehead dual of the generator βs=βsi1i0π2sp22s(V(1)), which defines the β–element βs. Let ξs,k=βs1ϖk. In this paper, we show that the composite of R L Cohen’s ζ–element ζn1 with ξs,n is nontrivial, where n>4 and 1<s<p1. As a corollary, ξs,n is also nontrivial for 1<s<p1.

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Xiugui Liu. "On R L Cohen's $\zeta$–element." Algebr. Geom. Topol. 11 (3) 1709 - 1735, 2011. https://doi.org/10.2140/agt.2011.11.1709

Information

Received: 13 July 2010; Revised: 24 February 2011; Accepted: 4 March 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1230.55009
MathSciNet: MR2821438
Digital Object Identifier: 10.2140/agt.2011.11.1709

Subjects:
Primary: 55Q45
Secondary: 55Q10

Rights: Copyright © 2011 Mathematical Sciences Publishers

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