R $\mathbb {R}$ -motivic stable stems

Pub Date : 2022-07-27 DOI:10.1112/topo.12256

Eva Belmont, Daniel C. Isaksen

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引用次数: 15

Abstract

We compute some $R$ -motivic stable homotopy groups. For $s - w ⩽ 11$ , we describe the motivic stable homotopy groups $π_{s, w}$ of a completion of the $R$ -motivic sphere spectrum. We apply the $ρ$ -Bockstein spectral sequence to obtain $R$ -motivic $Ext$ groups from the $C$ -motivic $Ext$ groups, which are well understood in a large range. These $Ext$ groups are the input to the $R$ -motivic Adams spectral sequence. We fully analyze the Adams differentials in a range, and we also analyze hidden extensions by $ρ$ , 2, and $η$ . As a consequence of our computations, we recover Mahowald invariants of many low-dimensional classical stable homotopy elements.

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R $\mathbb {R}$ -动力稳定系统

我们计算了一些R $\mathbb {R}$ -动力稳定同伦群。对于s−w≤11 $s - w \leqslant 11$，我们描述了动力稳定同伦群π s，w $\pi _{s,w}$完成了R $\mathbb {R}$ -动力球谱。我们应用ρ $\rho$ -Bockstein谱序列从C $\mathbb {C}$ -motivic Ext $\operatorname{Ext}$基得到R $\mathbb {R}$ -motivic Ext $\operatorname{Ext}$基，这在很大程度上是可以理解的。这些Ext $\operatorname{Ext}$组是R $\mathbb {R}$ -动机亚当斯光谱序列的输入。我们在一个范围内充分分析了Adams微分，我们还分析了ρ $\rho$, 2和η $\eta$的隐藏扩展。作为计算的结果，我们恢复了许多低维经典稳定同伦元素的Mahowald不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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