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$ \mathbb{Z}/2$-equivariant and $ \mathbb{R}$-motivic stable stems


Authors: Daniel Dugger and Daniel C. Isaksen
Journal: Proc. Amer. Math. Soc. 145 (2017), 3617-3627
MSC (2010): Primary 55Q10; Secondary 55Q91
DOI: https://doi.org/10.1090/proc/13505
Published electronically: February 21, 2017
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Abstract: We establish an isomorphism between the stable homotopy groups $ \hat {\pi }^{\mathbb{R}}_{s,w}$ of the 2-completed $ \mathbb{R}$-motivic sphere spectrum and the stable homotopy groups $ \hat {\pi }^{\mathbb{Z}/2}_{s,w}$ of the 2-completed $ \mathbb{Z}/2$-equivariant sphere spectrum, valid in the range $ s \geq 3 w - 5$ or $ s \leq -1$.


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Additional Information

Daniel Dugger
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: ddugger@math.uoregon.edu

Daniel C. Isaksen
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: isaksen@wayne.edu

DOI: https://doi.org/10.1090/proc/13505
Received by editor(s): March 30, 2016
Received by editor(s) in revised form: September 18, 2016
Published electronically: February 21, 2017
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2017 American Mathematical Society