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arXiv · 2011.08956

The 2-primary Hurewicz image of tmf

Mark Behrens·Mark Mahowald·J. D. Quigley
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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,v_1^8) using a modified form of the Adams spectral sequence and the tmf-resolution, and then proving the existence of a v_2^32-self map on M(8,v_1^8) to generate 192-periodic families in the stable homotopy groups of spheres.

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Mark Behrens, Mark Mahowald, J. D. Quigley. 2020-11-17. The 2-primary Hurewicz image of tmf. https://doi.org/10.2140/gt.2023.27.2763

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