ON THE DOUBLE TRANSFER AND THE f-INVARIANT

Abstract

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 ‫ރ‬P ∞ × ‫ރ‬P ∞ 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 MUhomology 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).