https://hal.univ-angers.fr/hal-03054052Powell, GeoffreyGeoffreyPowellLAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche ScientifiqueOn the double transfer and the f-invariantHAL CCSD2012PrimarySecondary[MATH] Mathematics [math]Univ Angers, Okina2020-12-11 11:47:332021-11-16 09:52:052020-12-11 11:47:33frJournal articles10.1017/S00170895120001581<p>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).</p>