paper

Euclidean lengths and the Culler-Shalen norms of slopes

arXiv:2507.09986

Abstract

In the study of exceptional Dehn fillings, two functions on slopes, called the Euclidean length on a horotorus and the Culler-Shalen norm, play important roles. In this paper, we investigate their relationship and establish two inequalities between them. As a byproduct, some bounds on the boundary slope diameter are given.

18 pages, 1 figure