Homology groups of $$$\mathbb{C}{\Omega}_n$$$ space for certain dimensionalities

A.M. Pas'ko (Oles Honchar Dnipropetrovsk National University)

Abstract


We calculate the homology groups $$$H_k(\mathbb{C}{\Omega}_n)$$$, $$$k = 0,1,2,2n-1,2n,2n+1$$$. We establish that the $$$\mathbb{C}{\Omega}_n$$$ space has a zero Euler characteristic.

Keywords


homology groups; CW complex; spline

References


Koshcheev V.A. "Fundamental groups of spaces of generalised perfect splines", Tr. In-ta matematiki i mekhaniki UrO RAN, 2009; 15(1): pp. 159-165. (in Russian)

Pas'ko A.M. "On homotopic groups of spaces of generalised perfect splines", Dnipr. Univ. Math. Bull., 2012; 17: pp. 138-140. (in Russian)

Pas'ko A.M. "Simple connectedness of one space of complex-valued functions", Dnipr. Univ. Math. Bull., 2015; 20: pp. 70-74. (in Ukrainian)

Ruban V.I. "Cellular partitioning of spaces of $$$\Omega$$$-splines", Researches on modern problems of summation and approximation of functions and their applications, Dnipropetrovsk, 1985; pp. 39-40. (in Russian)

Ruban V.I. "Cellular structure and cohomologies of spaces of generalised perfect splines", Dnipr. Univ. Math. Bull., 1999; 4: pp. 85-90. (in Russian)

Fomenko A.T., Fuks D.B. Course in homotopic topology, Moscow, 1989; 494 p. (in Russian)


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