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Towards the
$K(2)$–local homotopy groups of $Z$
Prasit Bhattacharya and Philip Egger |
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Algebraic & Geometric Topology 20 (2020) 1235–1277
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Abstract |
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Previously (Adv. Math. 360 (2020) art. id. 106895), we introduced a class of –local finite spectra and showed that all spectra admit a –self-map of periodicity . The aim here is to compute the –local homotopy groups of all spectra 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 –differentials and a few potential hidden –extensions, though we conjecture that all these differentials and hidden extensions are trivial. |
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Keywords
$K(2)$–local homotopy of $Z$, stable homotopy,
$v_2$–periodicity
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Mathematical Subject Classification 2010
Primary: 55N20, 55Q10, 55Q51
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References |
Publication
Received: 17 April 2018
Revised: 22 August 2019
Accepted: 6 September 2019
Published: 27 May 2020
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Authors |
| Prasit Bhattacharya | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| Philip Egger | |
| Center for Neuroprosthetics Swiss Federal Institute of Technology (EPFL) Geneva Switzerland |
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