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2016 The $\eta$–inverted $\mathbb{R}$–motivic sphere
Bertrand Guillou, Daniel Isaksen
Algebr. Geom. Topol. 16(5): 3005-3027 (2016). DOI: 10.2140/agt.2016.16.3005

Abstract

We use an Adams spectral sequence to calculate the –motivic stable homotopy groups after inverting η. The first step is to apply a Bockstein spectral sequence in order to obtain h1 –inverted –motivic Ext groups, which serve as the input to the η–inverted –motivic Adams spectral sequence. The second step is to analyze Adams differentials. The final answer is that the Milnor–Witt (4k1)–stem has order 2u+1, where u is the 2–adic valuation of 4k. This answer is reminiscent of the classical image of J. We also explore some of the Toda bracket structure of the η–inverted –motivic stable homotopy groups.

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Bertrand Guillou. Daniel Isaksen. "The $\eta$–inverted $\mathbb{R}$–motivic sphere." Algebr. Geom. Topol. 16 (5) 3005 - 3027, 2016. https://doi.org/10.2140/agt.2016.16.3005

Information

Received: 29 October 2015; Revised: 1 March 2016; Accepted: 29 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06653767
MathSciNet: MR3572357
Digital Object Identifier: 10.2140/agt.2016.16.3005

Subjects:
Primary: 14F42
Secondary: 55Q45, 55T15

Rights: Copyright © 2016 Mathematical Sciences Publishers

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