The homotopy groups $$$\pi_k(\Omega_n(m))$$$, $$$k=1,...,n$$$

A.M. Pasko

doi:10.15421/242519

The homotopy groups $$$\pi_k(\Omega_n(m))$$$, $$$k=1,...,n$$$

A.M. Pasko (Oles Honchar Dnipro National University)

Abstract

The paper continues the investigation of the spaces of complex-valued perfect splines $$$\Omega_n(m)$$$. These spaces were introduced as generalization of the spaces $$$\Omega_n$$$, the topology of which has been studied by V.I. Ruban, V.A. Koshcheev, A.M. Pasko. In our previous papers the homology groups of the spaces $$$\Omega_n(m)$$$ have been found and their simply connectedness was established. The topic of the paper is the homotopy groups $$$\pi_k(\Omega_n(m)), k=1,...,n$$$. They have been found using the homology groups of the spaces $$$\Omega_n(m)$$$, their simply connectedness and the Hurewicz isomorphism theorem.

Keywords

generalized perfect spline; the Hurewicz isomorphism theorem; homotopy groups

MSC 2020

Pri 55N10, Sec 41A99

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References

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Pasko A.M. "The homology groups of the space $$$\Omega_n(m)$$$", Res. Math., 2019; 27(1): pp. 39-44. doi:10.15421/241904

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