Tangles and the Stone-Cech compactification of infinite graphs

TL;DR

This paper demonstrates that the tangle space of an infinite graph, which provides a compactification, can be obtained as a quotient of its Stone-ach remainder by contracting connected components, linking tangles to topological compactifications.

Contribution

It establishes a novel connection between the tangle space of a graph and its Stone-ach compactification, showing they are related through a quotient process.

Findings

Tangle space is a quotient of the Stone-ach remainder.

Connected components are contracted to obtain the tangle space.

Provides a new topological perspective on infinite graph compactifications.

Abstract

We show that the tangle space of a graph, which compactifies it, is a quotient of its Stone-\v{C}ech remainder obtained by contracting the connected components.