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

Authors :
Hensel, Sebastian
Przytycki, Piotr
Webb, Richard C. H.
Source :
Journal of the European Mathematical Society (EMS Publishing); 2015, Vol. 17 Issue 4, p755-762, 8p
Publication Year :
2015

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. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
HYPERBOLIC functions
GRAPH theory
TRIANGLES
HOMOTOPY groups
GROMOV-Witten invariants

Details

Language :
English
ISSN :
14359855
Volume :
17
Issue :
4
Database :
Complementary Index
Journal :
Journal of the European Mathematical Society (EMS Publishing)
Publication Type :
Academic Journal
Accession number :
157509799
Full Text :
https://doi.org/10.4171/JEMS/517
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