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

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology 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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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.