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On the double transfer and the f-invariant

Abstract :

The purpose of this paper is to investigate the algebraic double S 1-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, Topology 38(2) (1999), 387–425).

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Soumis le : vendredi 11 décembre 2020 - 11:47:33
Dernière modification le : mardi 16 novembre 2021 - 09:52:05

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Geoffrey Powell. On the double transfer and the f-invariant. Glasgow Mathematical Journal, Cambridge University Press (CUP), 2012, 54 (03), pp.547 - 577. ⟨10.1017/S0017089512000158⟩. ⟨hal-03054052⟩



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