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- Title
Geometry of the augmented disk graph.
- Authors
MA, JIMING
- Abstract
For a handlebody H, we define two graphs, the augmented disk graph $\mathcal{ADG}(H)$ and the truncated augmented disk graph $\mathcal{TADG}(H)$, and we show they are hyperbolic in the sense of Gromov. In the process, we show they are quasi-isometric to two other disk graphs defined by U. Hamenstädt, the super conducting disk graph $\mathcal{SDG}(H)$ and the electrified disk graph $\mathcal{EDG}(H)$ respectively. So we reprove two theorems of Hamenstädt [12].Our approach uses techniques from Masur–Schleimer's study on the hyperbolicity of the disk graph $\mathcal{DG}(H)$ [21].
- Subjects
GRAPH theory; HANDLEBODIES; HYPERBOLIC functions; ISOMETRICS (Mathematics); MATHEMATICAL analysis
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2014, Vol 156, Issue 2, p363
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004113000716