Separating a chart

TL;DR

This paper establishes a condition under which a chart can be decomposed into a union of two disjointly supported charts, each contained in separate disks, and are related by C-move equivalence.

Contribution

It introduces a specific condition for a chart to be equivalent to a product of two disjoint charts, advancing understanding of chart decompositions.

Findings

Identifies a condition for chart decomposition into two disjoint charts.

Shows the equivalence of a chart to a product of two charts under certain conditions.

Provides a framework for analyzing chart structures in topological studies.

Abstract

In this paper, we shall show a condition for that a chart is C-move equivalent to the product of two charts, the union of two charts $\Gamma^*$ and $\Gamma^{**}$ which are contained in disks $D^*$ and $D^{**}$ with $D^*\cap D^{**}=\emptyset$.