1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs

Sebastian Hensel; Piotr Przytycki; Richard Webb

doi:10.4171/JEMS/517

1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs

Sebastian Hensel, Piotr Przytycki, Richard Webb

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	755-762
Number of pages	8
Journal	Journal of the European Mathematical Society
Volume	17
DOIs	https://doi.org/10.4171/JEMS/517
Publication status	Published - 9 Apr 2015

Keywords

Gromov hyperbolic
slim triangle
curve graph
arc graph
unicorn

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10.4171/JEMS/517

https://arxiv.org/pdf/1301.5577.pdf

Cite this

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title = "1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs",

abstract = "We describe unicorn paths in the arc graph and show that they form 1-slim triangles andare invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Consideringthe 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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AU - Przytycki, Piotr

AU - Webb, Richard

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N2 - We describe unicorn paths in the arc graph and show that they form 1-slim triangles andare invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Consideringthe same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic,including closed surfaces.

AB - We describe unicorn paths in the arc graph and show that they form 1-slim triangles andare invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Consideringthe same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic,including closed surfaces.

KW - Gromov hyperbolic

KW - slim triangle

KW - curve graph

KW - arc graph

KW - unicorn

U2 - 10.4171/JEMS/517

DO - 10.4171/JEMS/517

M3 - Article

SN - 1435-9855

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SP - 755

EP - 762

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

ER -

1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs

Abstract

Keywords

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