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2015 Quasigeodesic flows and sphere-filling curves
Steven Frankel
Geom. Topol. 19(3): 1249-1262 (2015). DOI: 10.2140/gt.2015.19.1249

Abstract

Given a closed hyperbolic 3–manifold M with a quasigeodesic flow, we construct a π1–equivariant sphere-filling curve in the boundary of hyperbolic space. Specifically, we show that any complete transversal P to the lifted flow on 3 has a natural compactification to a closed disc that inherits a π1–action. The embedding P3 extends continuously to the compactification, and restricts to a surjective π1–equivariant map P 3 on the boundary. This generalizes the Cannon–Thurston theorem, which produces such group-invariant space-filling curves for fibered hyperbolic 3–manifolds.

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Steven Frankel. "Quasigeodesic flows and sphere-filling curves." Geom. Topol. 19 (3) 1249 - 1262, 2015. https://doi.org/10.2140/gt.2015.19.1249

Information

Received: 22 July 2013; Revised: 25 February 2014; Accepted: 26 July 2014; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1327.57021
MathSciNet: MR3352235
Digital Object Identifier: 10.2140/gt.2015.19.1249

Subjects:
Primary: 57M60
Secondary: 37C27, 57M50

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2015
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