Higher homotopy normalities in topological groups

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2023-02-17 DOI:10.1112/topo.12282

Mitsunobu Tsutaya

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引用次数: 0

Abstract

The purpose of this paper is to introduce $N_{k} (ℓ)$ -maps ( $1 ⩽ k, ℓ ⩽ \infty$ ), which describe higher homotopy normalities, and to study their basic properties and examples. An $N_{k} (ℓ)$ -map is defined with higher homotopical conditions. It is shown that a homomorphism is an $N_{k} (ℓ)$ -map if and only if there exists fiberwise maps between fiberwise projective spaces with some properties. Also, the homotopy quotient of an $N_{k} (k)$ -map is shown to be an $H$ -space if its LS category is not greater than $k$ . As an application, we investigate when the inclusions $SU (m) \to SU (n)$ and $SO (2 m + 1) \to SO (2 n + 1)$ are $p$ -locally $N_{k} (ℓ)$ -maps.

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拓扑群中的高同伦规范性

本文的目的是介绍Nk(ℓ)$N_ k（\ell）$-maps（1⩽k，ℓ⩽∞$1\leqslant k，\ell\leqslant\infty$），并研究了它们的基本性质和例子。An Nk(ℓ)$N_k（\ell）$-map是用更高的同位条件定义的。证明了同态是Nk(ℓ)$N_k（\ell）$-map当且仅当在具有某些性质的纤维状投影空间之间存在纤维状映射。此外，如果Nk（k）$N_k（k）$映射的LS范畴不大于k$k$，则其同伦商被证明是H$H$空间。作为一个应用，我们研究了当夹杂物SU（m）→SU（n）$\运算符名称｛SU｝（m）\rightarrow\运算符名称{SU}（n）$和SO（2m+1）→SO（2n+1）$\运算符名称｛SO｝（2m+1）\rightarrow\运算符名称{SO｝(ℓ)$N_k（\ell）$映射。

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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.