- journal article metadata
European Mathematical Society Publishing House
2017-03-24 14:03:37
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
10
2016
4
The curves not carried
Vaibhav
Gadre
University of Glasgow, GLASGOW, UNITED KINGDOM
Saul
Schleimer
University of Warwick, COVENTRY, UNITED KINGDOM
Train tracks, curve complex, quasi-convex
Suppose $\tau$ is a train track on a surface $S$. Let $\mathcal C(\tau)$ be the set of isotopy classes of simple closed curves carried by $\tau$. Masur and Minsky [2004] prove that $\mathcal C(\tau)$ is quasi-convex inside the curve complex $\mathcal C(S)$. We prove that the complement, $\mathcal C(S) - \mathcal C(\tau)$, is quasi-convex.
Manifolds and cell complexes
Group theory and generalizations
Functions of a complex variable
1249
1264
10.4171/GGD/382
http://www.ems-ph.org/doi/10.4171/GGD/382