The curve complex and covers via hyperbolic 3-manifolds

Abstract

Rafi and Schleimer recently proved that the natural relation between curve complexes induced by a covering map between two surfaces is a quasi-isometric embedding. We offer another proof of this result using a distance estimate via hyperbolic 3-manifolds.

5 pages

Cited by in corpus (3)

• Cusp geometry of fibered 3-manifolds
• Covers of surfaces, Kleinian groups, and the curve complex
• Projections in the curve complex arising from covering maps