Abstract
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.
Citation
James W Cannon. William P Thurston. "Group invariant Peano curves." Geom. Topol. 11 (3) 1315 - 1355, 2007. https://doi.org/10.2140/gt.2007.11.1315
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