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$\mathrm{tmf}$–based Mahowald invariants

J D Quigley

Algebraic & Geometric Topology 22 (2022) 1789–1839
Abstract

The 2–primary homotopy β–family, defined as the collection of Mahowald invariants of Mahowald invariants of 2i for i 1, is an infinite collection of periodic elements in the stable homotopy groups of spheres. We calculate tmf –based approximations to this family. Our calculations combine an analysis of the Atiyah–Hirzebruch spectral sequence for the Tate construction of tmf with trivial C2–action and Behrens’ filtered Mahowald invariant machinery.

Keywords
tmf, Mahowald invariant, root invariant, Greek letter elements
Mathematical Subject Classification 2010
Primary: 55P42
Secondary: 55Q45, 55Q51
References
Publication
Received: 13 December 2019
Revised: 27 April 2021
Accepted: 19 May 2021
Published: 10 October 2022
Authors
J D Quigley
Department of Mathematics
Cornell University
Ithaca, NY
United States
Max Planck Institute for Mathematics
Bonn
Germany
https://quigleyjd.github.io/