The curve complex has dead ends

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

No reviews yet.

No comments yet.