Geodesic
Counting arcs on hyperbolic surfaces
Nick Bell1
1University of Kent, UK
Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 459-478

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DOI

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.
DOI : 10.4171/ggd/705
Classification : 32-XX, 53-XX
Mots-clés : arc, orthogeodesic, cusp, mapping class group

Nick Bell  1

1 University of Kent, UK 
Nick Bell. Counting arcs on hyperbolic surfaces. Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 459-478. doi: 10.4171/ggd/705
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