Year: 2025
Type: article
Abstract: We describe an algorithm which, given two essential curves on a surface S, computes their distance in the curve graph of S, up to multiplicative and additive errors. As an application, we present an algorithm to decide the Nielsen–Thurston type (periodic, reducible, or pseudo-Anosov) of a mapping class of S. The novelty of our algorithms lies in the fact that their running time is polynomial in the size of the input and in the complexity of S—say, its Euler characteristic. This is in contrast with previously known algorithms, which run in polynomial time in the size of the input for any fixed surface S.
Source: Mathematische Annalen
Author: Filippo Baroni
Institution: University of Oxford
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4410062148