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arXiv · 1210.6698

The curve complex has dead ends

Joan S. Birman·William W. Menasco
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Abstract

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.

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Joan S. Birman, William W. Menasco. 2014-04-10. The curve complex has dead ends. https://doi.org/10.1007/s10711-014-9978-y

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