English

The 2-primary Hurewicz image of tmf

Algebraic Topology 2023-09-27 v4

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.

Keywords

Cite

@article{arxiv.2011.08956,
  title  = {The 2-primary Hurewicz image of tmf},
  author = {Mark Behrens and Mark Mahowald and J. D. Quigley},
  journal= {arXiv preprint arXiv:2011.08956},
  year   = {2023}
}

Comments

61 pages, 12 figures. v4: made corrections based on comments from referees