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The $2$–primary Hurewicz image of tmf

Mark Behrens, Mark Mahowald and J D Quigley

Geometry & Topology 27 (2023) 2763–2831
Abstract

We determine the image of the 2–primary tmf Hurewicz homomorphism, where tmf is the spectrum of topological modular forms. We do this by lifting elements of tmf to the homotopy groups of the generalized Moore spectrum M(8,v18) using a modified form of the Adams spectral sequence and the tmf resolution, and then proving the existence of a v232–self-map on M(8,v18) to generate 192–periodic families in the stable homotopy groups of spheres.

Keywords
topological modular forms, tmf, Hurewicz image, $v_2$–periodicity, tmf resolution
Mathematical Subject Classification 2010
Primary: 55Q45
Secondary: 55Q51, 55T15
References
Publication
Received: 17 February 2021
Revised: 18 November 2021
Accepted: 22 December 2021
Published: 19 September 2023
Proposed: Haynes R Miller
Seconded: Stefan Schwede, Jesper Grodal
Authors
Mark Behrens
Department of Mathematics
University of Notre Dame
Notre Dame, IN
United States
Mark Mahowald
Department of Mathematics
Northwestern University
Evanston, IL
United States
J D Quigley
Department of Mathematics
University of Virginia
Charlottesville, VA
United States

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