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

Abstract

top
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.

How to cite

top

Hensel, 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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.