Towards the K(2)–local homotopy groups of Z

Bhattacharya, Prasit¹ ; Egger, Philip²

¹Department of Mathematics, University of Virginia, Charlottesville, VA, United States
²Center for Neuroprosthetics, Swiss Federal Institute of Technology (EPFL), Geneva, Switzerland

Algebraic and Geometric Topology, Tome 20 (2020) no. 3, pp. 1235-1277

Résumé

Previously (Adv. Math. 360 (2020) art. id. 106895), we introduced a class 𝒵˜ of 2–local finite spectra and showed that all spectra Z ∈𝒵˜ admit a v2–self-map of periodicity  1. The aim here is to compute the K(2)–local homotopy groups π∗LK(2)Z of all spectra Z ∈𝒵˜ using a homotopy fixed point spectral sequence, and we give an almost complete answer. The incompleteness lies in the fact that we are unable to eliminate one family of d3–differentials and a few potential hidden 2–extensions, though we conjecture that all these differentials and hidden extensions are trivial.

Détail

DOI : 10.2140/agt.2020.20.1235

Classification : 55N20, 55Q10, 55Q51
Keywords: $K(2)$–local homotopy of $Z$, stable homotopy, $v_2$–periodicity

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