The homology groups $H_{n+1} \left( \mathbb{C}\Omega_n \right)$

The topic of the paper is investigation homology groups $(2n+1)$-dimensional CW-complex $\mathbb{C}\Omega_n$. spaces $\mathbb{C}\Omega_n$ consist complex-valued functions and are analogue $\Omega_n$, widely known in approximation theory. have been introduced 2015 by A.M. Pasko who has built CW-structure using this established that simply connected. Note mentioned $\Omega_n$ constructed V.I. Ruban. Further found space dimensionalities $0, 1, \ldots, n, 2n-1, 2n, 2n+1$. goal present to find group $H_{n+1}\left ( \mathbb{C}\Omega_n \right )$. It proved $H_{n+1} \left )=\mathbb{Z}^\frac{n+1}{2}$ if $n$ odd )=\mathbb{Z}^\frac{n+2}{2}$ even.