Geometry & Topology
- Geom. Topol.
- Volume 11, Number 3 (2007), 1315-1355.
Group invariant Peano curves
Our main theorem is that, if is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre and pseudo-Anosov monodromy, then the lift of the inclusion of in to universal covers extends to a continuous map of to , where . The restriction to maps onto and gives an example of an equivariant –filling Peano curve. After proving the main theorem, we discuss the case of the figure-eight knot complement, which provides evidence for the conjecture that the theorem extends to the case when is a once-punctured hyperbolic surface.
Geom. Topol., Volume 11, Number 3 (2007), 1315-1355.
Received: 12 August 1999
Revised: 12 April 2007
Accepted: 12 April 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensions 57N05: Topology of $E^2$ , 2-manifolds 57N60: Cellularity
Cannon, James W; Thurston, William P. Group invariant Peano curves. Geom. Topol. 11 (2007), no. 3, 1315--1355. doi:10.2140/gt.2007.11.1315. https://projecteuclid.org/euclid.gt/1513799898