The homology groups $H_{n+1} \left( \mathbb{C}\Omega_n \right)$
| Autor: | A.M. Pasko |
|---|---|
| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Researches in Mathematics, Vol 30, Iss 2, Pp 30-33 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2664-4991 2664-5009 |
| DOI: | 10.15421/242210 |
| Popis: | The topic of the paper is the investigation of the homology groups of the $(2n+1)$-dimensional CW-complex $\mathbb{C}\Omega_n$. The spaces $\mathbb{C}\Omega_n$ consist of complex-valued functions and are the analogue of the spaces $\Omega_n$, widely known in the approximation theory. The spaces $\mathbb{C}\Omega_n$ have been introduced in 2015 by A.M. Pasko who has built the CW-structure of the spaces $\mathbb{C}\Omega_n$ and using this CW-structure established that the spaces $\mathbb{C}\Omega_n$ are simply connected. Note that the mentioned CW-structure of the spaces $\mathbb{C}\Omega_n$ is the analogue of the CW-structure of the spaces $\Omega_n$ constructed by V.I. Ruban. Further A.M. Pasko found the homology groups of the space $\mathbb{C}\Omega_n$ in the dimensionalities $0, 1, \ldots, n, 2n-1, 2n, 2n+1$. The goal of the present paper is to find the homology group $H_{n+1}\left ( \mathbb{C}\Omega_n \right )$. It is proved that $H_{n+1} \left ( \mathbb{C}\Omega_n \right )=\mathbb{Z}^\frac{n+1}{2}$ if $n$ is odd and $H_{n+1} \left ( \mathbb{C}\Omega_n \right )=\mathbb{Z}^\frac{n+2}{2}$ if $n$ is even. |
| Databáze: | Directory of Open Access Journals |
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