The Gordian graph is one-ended

A. Yu. Miller<sup>ab

a</sup> St. Petersburg Department of Steklov Institute of Mathematics
^b St. Petersburg State University

Abstract: In 2005, Gambaudo and Ghys posed the question of studying the behavior at infinity of the Gordian graph by analyzing the “ends” – the unbounded connected components of the complements of bounded subsets. We completely answer this question by proving that the Gordian graph has exactly one end.

Key words and phrases: knot theory, Gordian graph, crossing change, ends.

UDC: 515.162.86

Received: 02.12.2025

Language: English