The relative James construction and its application to homotopy groups

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-08-14 DOI:10.1016/j.topol.2024.109043

Zhongjian Zhu, Tian Jin

引用次数: 0

Abstract

In this paper, we develop the new method to compute the homotopy groups of the mapping cone $C_{f} = Y \cup_{f} C X$ beyond the metastable range by analysing the homotopy of the n-th filtration of the relative James construction $J (X, A)$ for CW-pair $A \overset{i}{↪} X$ , defined by B. Gray, which is homotopy equivalent to the homotopy fiber of the pinch map $X \cup_{i} C A \to Σ A$ . As an application, we compute the 5 and 6-dim unstable homotopy groups of 3-dimensional mod $2^{r}$ Moore spaces for all positive integers r.

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相对詹姆斯构造及其在同调群中的应用

在本文中，我们通过分析 B. 格雷定义的 CW 对 AiX 的相对詹姆斯构造 J(X,A) 的 n-th 滤波的同调，发展了计算映射锥 Cf=Y∪fCX 超越可变范围的同调群的新方法，该方法等同于捏合映射 X∪iCA→ΣA 的同调纤维。作为应用，我们计算了所有正整数 r 的 3 维 mod 2r 摩尔空间的 5 维和 6 维不稳定同调群。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.