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ON THE DOUBLE TRANSFER AND THE f-INVARIANT

Published online by Cambridge University Press:  30 March 2012

GEOFFREY POWELL
GEOFFREY POWELL*
Affiliation:
Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France e-mail: powell@math.univ-paris13.fr
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Abstract

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The purpose of this paper is to investigate the algebraic double S1-transfer, in particular the classes in the two-line of the Adams–Novikov spectral sequence which are the image of comodule primitives of the MU-homology of ℂP∞ × ℂP∞ via the algebraic double transfer. These classes are analysed by two related approaches: the first, p-locally for p ≥ 3, by using the morphism induced in MU-homology by the chromatic factorisation of the double transfer map together with the f′-invariant of Behrens (for p ≥ 5) (M. Behrens, Congruences between modular forms given by the divided β-family in homotopy theory, Geom. Topol.13(1) (2009), 319–357). The second approach (after inverting 6) uses the algebraic double transfer and the f-invariant of Laures (G. Laures, The topological q-expansion principle, Topology38(2) (1999), 387–425).

Keywords

Primary 55R12Secondary 55N3455P42
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 547 - 577
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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