1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs (Q2344496)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs |
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1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs (English)
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15 May 2015
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Summary: We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.
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Gromov hyperbolic
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slim triangle
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curve graph
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arc graph
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unicorn
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