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

Sebastian Hensel; Piotr Przytycki; Richard C. H. Webb

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 4, page 755-762
- ISSN: 1435-9855

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topHensel, Sebastian, Przytycki, Piotr, and Webb, Richard C. H.. "1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs." Journal of the European Mathematical Society 017.4 (2015): 755-762. <http://eudml.org/doc/277700>.

@article{Hensel2015,

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.},

author = {Hensel, Sebastian, Przytycki, Piotr, Webb, Richard C. H.},

journal = {Journal of the European Mathematical Society},

keywords = {Gromov hyperbolic; slim triangle; curve graph; arc graph; unicorn; Gromov hyperbolic; slim triangle; curve graph; arc graph; unicorn},

language = {eng},

number = {4},

pages = {755-762},

publisher = {European Mathematical Society Publishing House},

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

url = {http://eudml.org/doc/277700},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Hensel, Sebastian

AU - Przytycki, Piotr

AU - Webb, Richard C. H.

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

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 4

SP - 755

EP - 762

AB - 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.

LA - eng

KW - Gromov hyperbolic; slim triangle; curve graph; arc graph; unicorn; Gromov hyperbolic; slim triangle; curve graph; arc graph; unicorn

UR - http://eudml.org/doc/277700

ER -

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