空间n(m)的基本群

Q4 Mathematics Researches in Mathematics Pub Date : 2022-07-04 DOI:10.15421/242207
A. Paśko
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引用次数: 0

摘要

本文考虑了空间$\Omega_n(m)$。空间$\Omega_n(m)$,于2018年由A.M.Pasko和Y.O. Orekhova,是空间$\Omega_n$的泛化(空间$\Omega_n(2)$与$\Omega_n$重合)关于空间$\Omega_n$的同伦性质的研究是由V.I. Ruban在1985年开始的,随后V.A. Koshcheev, A.M.Pasko。特别是V.A. Koshcheev证明了空间$\Omega_n$是单连通的。我们推广了这个结果,证明了所有的空间$\Omega_n(m)$都是单连通的。为了证明空间的简单连通性,我们考虑这个空间的1-骨架。使用1单元格,我们形成闭合的方式来创建空间的基本群$\Omega_n(m)$。我们用2单元格证明了所有这些闭合路径都等价于平凡路径。所以空间n(m)的基本群是平凡的空间n(m)是单连通的。
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The fundamental group of the space $\Omega_n(m)$
In the present paper the spaces $\Omega_n(m)$ are considered. The spaces $\Omega_n(m)$, introduced in 2018 by A.M. Pasko and Y.O. Orekhova, are the generalization of the spaces $\Omega_n$ (the space $\Omega_n(2)$ coincides with $\Omega_n$). The investigation of homotopy properties of the spaces $\Omega_n$ has been started by V.I. Ruban in 1985 and followed by V.A. Koshcheev, A.M. Pasko. In particular V.A. Koshcheev has proved that the spaces $\Omega_n$ are simply connected. We generalized this result proving that all the spaces $\Omega_n(m)$ are simply connected. In order to prove the simply connectedness of the space $\Omega_n(m)$ we consider the 1-skeleton of this space. Using 1-cells we form the closed ways that create the fundamental group of the space $\Omega_n(m)$. Using 2-cells we show that all these closed ways are equivalent to the trivial way. So the fundamental group of the space $\Omega_n(m)$ is trivial and the space $\Omega_n(m)$ is simply connected.
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来源期刊
CiteScore
0.50
自引率
0.00%
发文量
8
审稿时长
16 weeks
期刊最新文献
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