The curve complex has dead ends

Abstract

It is proved that the curve graph $C^1(\Sigma )$ of a surface ${\Sigma }_{g,n}$ has a local pathology that had not been identified as such: there are vertices $\alpha ,\beta$ in $C^1(\Sigma )$ such that $\beta$ is a dead end of every geodesic joining $\alpha$ to $\beta$. It also has double dead-ends. Every dead end has depth 1.

Final version, published on-line in Geometriae Dedicata. 4 pages, 1 figure

References in corpus (1)

• Geometry of the Complex of Curves I: Hyperbolicity

Cited by in corpus (1)

• Coloring curves on surfaces