A construction of noncontractible simply connected cell-like two dimensional Peano continua

TL;DR

The paper introduces a functorial method using the topologist sine curve to construct simply connected, noncontractible, cell-like Peano continua from noncontractible Peano continua, including a 2D example from the circle.

Contribution

It provides a novel functorial construction of simply connected, noncontractible, cell-like Peano continua from given noncontractible Peano continua, expanding the toolkit in topological continuum theory.

Findings

Constructs noncontractible simply connected 2D Peano continuum from circle

Provides a functorial method applicable to all noncontractible Peano continua

Demonstrates the existence of higher-dimensional noncontractible simply connected continua

Abstract

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts by a noncontractible n-dimensional Peano continuum for any n>0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting with the circle $\mathbb{S}^1$, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.