Higher homotopy normalities in topological groups
Higher homotopy normalities in topological groups
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拓扑群中更高的同伦正态性
DOI：
10.1112/topo.12282
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发表时间：
2023
影响因子：
1.1
通讯作者：
Tsutaya Mitsunobu
中科院分区：
文献类型：
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作者：
新屋良磨;山口勇太郎;中村誠希;陰山真矢;Sin’ya Ryoma;陰山真矢;陰山真矢;Sin’Ya Ryoma;新屋良磨;Ryoma Sin'ya;Ryoma Sin'ya;Ryoma Sin'ya;Tsutaya Mitsunobu
引入了描述高阶同伦的Nk（k）$Nk（\ell）$-映射（1 k，n k ∞ $1\leqslane k，\ell \leqslane\infty$），研究了它们的基本性质和例子.在更高的同伦条件下定义了Nk（n）$N_k（\ell）$-映射.证明了同态是Nk（n）$N_k（\ell）$-映射当且仅当纤维投射空间之间存在纤维映射并具有某些性质.同时，证明了一个Nk（k）$N_k（k）$-映射的同伦商是一个H$H$-空间，如果它的LS范畴不大于k$k$。作为应用，我们研究了包含SU（m）→SU（n）$\operatorname{SU}（m）\rightarrow \operatorname{SU}（n）$和SO（2 m +1）→SO（2n+1）$\operatorname {SO}（2 m +1）\rightarrow \operatorname{SO}（2n+1）$是p$p$-局部Nk（n）$N_k（\ell）$-映射的情形.
The purpose of this paper is to introduce Nk(ℓ)$N_k(\ell )$‐maps (1⩽k,ℓ⩽∞$1\leqslant k,\ell \leqslant \infty$), which describe higher homotopy normalities, and to study their basic properties and examples. An Nk(ℓ)$N_k(\ell )$‐map is defined with higher homotopical conditions. It is shown that a homomorphism is an Nk(ℓ)$N_k(\ell )$‐map if and only if there exists fiberwise maps between fiberwise projective spaces with some properties. Also, the homotopy quotient of an Nk(k)$N_k(k)$‐map is shown to be an H$H$‐space if its LS category is not greater than k$k$. As an application, we investigate when the inclusions SU(m)→SU(n)$\operatorname{SU}(m)\rightarrow \operatorname{SU}(n)$ and SO(2m+1)→SO(2n+1)$\operatorname{SO}(2m+1)\rightarrow \operatorname{SO}(2n+1)$ are p$p$‐locally Nk(ℓ)$N_k(\ell )$‐maps.