English

Polynomial-time algorithms for the curve graph

Geometric Topology 2016-10-05 v2

Abstract

We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can use these geodesics to compute the asymptotic translation length, Nielsen--Thurston type, and canonical curve system of a mapping class in polynomial time in its word length.

Keywords

Cite

@article{arxiv.1609.09392,
  title  = {Polynomial-time algorithms for the curve graph},
  author = {Mark C. Bell and Richard C. H. Webb},
  journal= {arXiv preprint arXiv:1609.09392},
  year   = {2016}
}

Comments

27 pages, 10 figures

R2 v1 2026-06-22T16:05:33.350Z