An unstable approach to the May-Lawrence matrix Toda bracket and the 2nd James-Hopf invariant

IF 0.6 4区 数学 Q3 MATHEMATICS
Juxin Yang , Toshiyuki Miyauchi , Juno Mukai
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引用次数: 0

Abstract

In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool to detect the unstable phenomena. Then, we give a generalization of the classical isomorphisms between homotopy groups of (JSm,Sm) and (JS2m,) localized at 2. After that we provide a generalized H-formula for matrix Toda brackets. As an application, we show a new construction of κ¯π26(S6) localized at 2 which improves the construction of κ¯ given by [4].

梅-劳伦斯矩阵托达括号和詹姆斯-霍普夫第二不变式的不稳定方法
在本文中,我们给出了梅-劳伦斯矩阵托达括号的不稳定方法,它成为探测不稳定现象的有用工具。然后,我们给出了同调群和局部在 2 之间经典同构的广义化。作为一种应用,我们展示了一种新的局部 2 的构造,它改进了......给出的局部 2 的构造。
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来源期刊
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.
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