Volume 16 (2009)

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β–family congruences and the f–invariant

Mark Behrens and Gerd Laures

Geometry & Topology Monographs 16 (2009) 9–29

DOI: 10.2140/gtm.2009.16.9

Abstract

In previous work, the authors have each introduced methods for studying the 2–line of the p–local Adams–Novikov spectral sequence in terms of the arithmetic of modular forms. We give the precise relationship between the congruences of modular forms introduced by the first author with the Q–spectrum and the f–invariant of the second author. This relationship enables us to refine the target group of the f–invariant in a way which makes it more manageable for computations.

Keywords

stable homotopy groups of spheres, topological modular forms, f-invariant

Mathematical Subject Classification

Primary: 55T15

Secondary: 11F11, 55P42

References
Publication

Received: 5 September 2008
Revised: 14 November 2008
Accepted: 2 December 2008
Published: 16 June 2009

Authors
Mark Behrens
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, Ma 02139-4307
USA
Gerd Laures
Fakultät für Mathematik
Ruhr-Universität Bochum, NA1/66
D-44780 Bochum
Germany