Group invariant Peano curves

By James W. Cannon, William P. Thurston. 2007

175 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b84b53bfe247bcbe524fd935379ebd84cedf5899

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In Computational Theory and Mathematics

1. D. Fisher
2. Mahan Mj
3. Michael Kapovich
4. Danny Calegari

In Discrete Mathematics and Combinatorics

1. D. Fisher
2. Mahan Mj
3. Michael Kapovich
4. Danny Calegari
5. Christoph Schwer
6. Arun Ram

In Geometry and Topology

1. Mahan Mj
2. Michael Kapovich
3. Danny Calegari
4. D. Fisher
5. J. Porti
6. B. Leeb
7. Anna Wienhard
8. Jean-Marc Schlenker

Citations in the corpus

• Expanding Thurston Maps (2010, unknown): “Cannon-Thurston construct (in [CT07]) an invariant Peano curve γ : S → S for the fundamental group of a (hyperbolic) 3-manifold M that fibers over the circle.”
• KLEINIAN GROUPS IN HIGHER DIMENSIONS (2007, background): “s of geometrically infinite Kleinian groups can be more complicated. A dendroid is a compact locally connected simply-connected 1-dimensional topological space. Theorem 8.5. (J. Cannon and W. Thurston [50], see also [1] and [57].) There exist singly-degenerate Kleinian groups whose limit sets are den”
• Foliations and the Geometry of 3-Manifolds (2007, methodology): “(Cannon–Thurston, Continuity of Peano map [44]) Suppose Mφ is a hyperbolic surface bundle over S1 with fiber Σ and monodromy φ.”
• Cannon-Thurston Maps for Surface Groups (2006, background): “In [Abi76], Abikoff gave an approach to a negative answer to Question 1.3. However, around 1980, Thurston realized that this approach would not work. Then, in a foundational paper, Cannon and Thurston [CT85] gave the first examples furnishing a positive answer to Question 1.1 for geometrically infinite”
• Groups acting on manifolds: around the Zimmer program (2008, background): “here are equivariant space filling curves, but they seem quite special. They arise as surface group equivariant maps from the circle to S2 and come from three manifolds which fiber over the circle, see [33]. 8. Representations of fundamental groups and arithmetic quotients In this section we discuss s”