tmf–based Mahowald invariants

Quigley, J D

doi:10.2140/agt.2022.22.1789

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$\mathrm{tmf}$–based Mahowald invariants

J D Quigley

Algebraic & Geometric Topology 22 (2022) 1789–1839

DOI: 10.2140/agt.2022.22.1789

Abstract

The $2$ –primary homotopy $β$ –family, defined as the collection of Mahowald invariants of Mahowald invariants of $2^{i}$ for $i \geq 1$ , 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 $C_{2}$ –action and Behrens’ filtered Mahowald invariant machinery.

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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/

Volume 22, issue 4 (2022)