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The
$2$–primary Hurewicz image of tmf
Mark Behrens, Mark Mahowald and J D Quigley |
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Geometry & Topology 27 (2023) 2763–2831
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Abstract |
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We determine the image of the –primary tmf Hurewicz homomorphism, where tmf is the spectrum of topological modular forms. We do this by lifting elements of to the homotopy groups of the generalized Moore spectrum using a modified form of the Adams spectral sequence and the tmf resolution, and then proving the existence of a –self-map on to generate –periodic families in the stable homotopy groups of spheres. |
Keywords
topological modular forms, tmf, Hurewicz image,
$v_2$–periodicity, tmf resolution
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Mathematical Subject Classification 2010
Primary: 55Q45
Secondary: 55Q51, 55T15
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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
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Authors |
| Mark Behrens | |
| Department of Mathematics University of Notre Dame Notre Dame, IN United States |
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| Mark Mahowald | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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| J D Quigley | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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