The 2–primary Hurewicz image of tmf

Behrens, Mark¹ ; Mahowald, Mark² ; Quigley, J D³

¹ Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States
² Department of Mathematics, Northwestern University, Evanston, IL, United States
³ Department of Mathematics, University of Virginia, Charlottesville, VA, United States

Geometry & topology, Tome 27 (2023) no. 7, pp. 2763-2831.

Résumé

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 ${\mathrm{tmf}}_{\ast }$ 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.

Détail

DOI : 10.2140/gt.2023.27.2763

Classification : 55Q45, 55Q51, 55T15
Keywords: topological modular forms, tmf, Hurewicz image, $v_2$–periodicity, tmf resolution

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