Group invariant Peano curves

2007/07/20 by J. W. Cannon, William P. Thurston · 5 citations
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Advanced Combinatorial Mathematics #Mathematics #Peano axioms #Invariant (physics) #Pure mathematics #Group (periodic table) #Mathematical analysis #Discrete mathematics

paper · pdf · doi:10.2140/gt.2007.11.1315

openalex publication_date 2007/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Our main theorem is that, if M is a closed hyperbolic 3-manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to universal covers extends to a continuous map of B 2 to B 3 , where

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
• Bouts des Varietes Hyperboliques de Dimension 3
• The combinatorial structure of cocompact discrete hyperbolic groups

Cited by

• Quasigeodesic flows and sphere-filling curves
• Geometric inflexibility and 3-manifolds that fiber over the circle
• Ideal boundaries of pseudo-Anosov flows and uniform convergence groups with connections and applications to large scale geometry
• Cannon–Thurston maps for pared manifolds of bounded geometry
• Small curvature laminations in hyperbolic 3–manifolds
• Kleinian group [wikipedia]
• Space-filling curve [wikipedia]

Related

• A note on covers of fibred hyperbolic manifolds
• Fibering rigidity of 3-manifolds with Torelli monodromy
• Linear progress in fibres
• On the degree of a finite cover which fibers over circle
• Zippers