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Glasgow Mathematical Journal (1)

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ON THE DOUBLE TRANSFER AND THE f-INVARIANT
GEOFFREY POWELL
Journal:

Glasgow Mathematical Journal / Volume 54 / Issue 3 / September 2012

Published online by Cambridge University Press:

30 March 2012, pp. 547-577

Print publication:

September 2012
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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).