On the singular homology of one class of simply-connected cell-like spaces

TL;DR

This paper investigates the higher-dimensional homology and homotopy properties of a class of simply-connected, cell-like spaces called Snake spaces, extending previous constructions and functorial analyses.

Contribution

It introduces a functorial approach to analyze the homology and homotopy of spaces derived from compact spaces, generalizing earlier Snake space examples.

Findings

Higher-dimensional homology groups of $SC(Z, ullet)$ are characterized.

Homotopy properties of $SC(Z, ullet)$ are analyzed for various $Z$.

Extension of Snake space concepts to broader classes of spaces.

Abstract

In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called {\sl Snake space}. In the sequel we introduced the functor $SC(-,-)$ defined on the category of all spaces with base points and continuous mappings. For the circle $S^1$, the space $SC(S^1, \ast)$ is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces $SC(Z, \ast)$ for any path-connected compact spaces $Z$.