On the second homotopy group of $SC(Z)$

TL;DR

This paper investigates the algebraic properties of the space $SC(Z)$, a cone-like construction introduced earlier, focusing on its second homotopy group to understand its topological complexity.

Contribution

The paper provides new algebraic insights into the second homotopy group of the space $SC(Z)$, expanding understanding of its topological structure.

Findings

Determined the structure of the second homotopy group of $SC(Z)$

Established conditions under which $SC(Z)$ has certain algebraic properties

Extended previous work on the topology of cone-like spaces

Abstract

In our earlier paper (K. Eda, U. Karimov, and D. Repov\v{s}, \emph{A construction of simply connected noncontractible cell-like two-dimensional Peano continua}, Fund. Math. \textbf{195} (2007), 193--203) we introduced a cone-like space $SC(Z)$. In the present note we establish some new algebraic properties of $SC(Z)$.