|
|||||
|
|
|
|
|
|
|
|
|
The $\eta$–inverted
$\mathbb{R}$–motivic sphere
Bertrand J Guillou and Daniel C Isaksen |
|
Algebraic & Geometric Topology 16 (2016) 3005–3027
|
Abstract |
|
We use an Adams spectral sequence to calculate the –motivic stable homotopy groups after inverting . The first step is to apply a Bockstein spectral sequence in order to obtain –inverted –motivic groups, which serve as the input to the –inverted –motivic Adams spectral sequence. The second step is to analyze Adams differentials. The final answer is that the Milnor–Witt –stem has order , where is the –adic valuation of . This answer is reminiscent of the classical image of . We also explore some of the Toda bracket structure of the –inverted –motivic stable homotopy groups. |
Keywords
motivic homotopy theory, stable homotopy group,
eta-inverted stable homotopy group, Adams spectral sequence
|
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 55T15, 55Q45
|
References |
Publication
Received: 29 October 2015
Revised: 1 March 2016
Accepted: 29 March 2016
Published: 7 November 2016
|
Authors |
| Bertrand J Guillou | |
| Department of Mathematics University of Kentucky 715 Patterson Office Tower Lexington, KY 40506-0027 United States |
|
| Daniel C Isaksen | |
| Department of Mathematics Wayne State University 656 W Kirby Detroit, MI 48202 United States |
|
|
