New families in the homotopy of the motivic sphere spectrum
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- by Michael J. Andrews PDF
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Abstract:
Using iterates of the Adams self map $v_1^4:\Sigma ^8 S/2\longrightarrow S/2$ one can construct infinite families of elements in the stable homotopy groups of spheres, the $v_1$-periodic elements of order $2$. In this paper we work motivically over $\mathbb {C}$ and construct a non-nilpotent self map $w_1^4:\Sigma ^{20,12}S/\eta \longrightarrow S/\eta$. We then construct some infinite families of elements in the homotopy of the motivic sphere spectrum, $w_1$-periodic elements killed by $\eta$.References
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Additional Information
- Michael J. Andrews
- Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555
- Email: mjandr@math.ucla.edu
- Received by editor(s): June 29, 2017
- Received by editor(s) in revised form: August 20, 2017
- Published electronically: February 16, 2018
- Communicated by: Michael A. Mandell
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2711-2722
- MSC (2010): Primary 55Q45, 55Q51, 55T15, 14F42
- DOI: https://doi.org/10.1090/proc/13940
- MathSciNet review: 3778171
Dedicated: Dedicated to the memory of Amelia Perry.