Skip to main content
Kent Academic Repository

Counting arcs on hyperbolic surfaces

Bell, Nick (2023) Counting arcs on hyperbolic surfaces. Groups, Geometry, and Dynamics, 17 (2). pp. 459-478. ISSN 1661-7207. (doi:10.4171/ggd/705) (KAR id:100562)


We give the asymptotic growth of the number of arcs of bounded length between boundary components on hyperbolic surfaces with boundary. Specifically, if S has genus g,n boundary components and p punctures, then the number of orthogeodesic arcs in each pure mapping class group orbit of length at most L is asymptotic to L6g−6+2(n+p) times a constant. We prove an analogous result for arcs between cusps, where we define the length of such an arc to be the length of the sub-arc obtained by removing certain cuspidal regions from the surface.

Item Type: Article
DOI/Identification number: 10.4171/ggd/705
Uncontrolled keywords: Discrete Mathematics and Combinatorics, Geometry and Topology
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
SWORD Depositor: JISC Publications Router
Depositing User: JISC Publications Router
Date Deposited: 22 Mar 2023 14:15 UTC
Last Modified: 16 May 2023 10:21 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.