Geodesic
The curves not carried
Vaibhav Gadre1 orcid ; Saul Schleimer2 orcid
1University of Warwick, Coventry, UK
2University of Warwick, Coventry, UK
Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1249-1264

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DOI

Suppose τ is a train track on a surface S. Let C(τ) be the set of isotopy classes of simple closed curves carried by τ. Masur and Minsky [2004] prove that C(τ) is quasi-convex inside the curve complex C(S). We prove that the complement, C(S)−C(τ), is quasi-convex.
DOI : 10.4171/ggd/382
Classification : 57-XX, 20-XX, 30-XX
Mots-clés : Train tracks, curve complex, quasi-convex

Vaibhav Gadre  1   ; Saul Schleimer  2

1 University of Warwick, Coventry, UK
2 University of Warwick, Coventry, UK 
Vaibhav Gadre; Saul Schleimer. The curves not carried. Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1249-1264. doi: 10.4171/ggd/382
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