25 citations · 137 across the 30 of their papers we have counts for
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Hitchin representations of Fuchsian groups
Richard Canary
We survey the theory of Hitchin representations of Fuchsian groups and describe a conjectural geometric picture of an augmented Hitchin component.
Pressure metrics for deformation spaces of quasifuchsian groups with parabolics
Harrison Bray, Richard Canary, Lien-Yung Kao
In this paper, we produce a mapping class group invariant pressure metric on the space QF(S) of quasiconformal deformations of a co-finite area Fuchsian group uniformizing a surfac…
Topological restrictions on Anosov representations
Richard Canary, Konstantinos Tsouvalas
We characterize groups admitting Anosov representations into , projective Anosov representations into , and Borel Anosov represe…
Local topology in deformation spaces of hyperbolic 3-manifolds II
Jeffrey Brock, Kenneth Bromberg, Richard Canary +2
We prove that the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold with incompressible boundary is locally connected…
Simple Length Rigidity for Hitchin Representations
Martin Bridgeman, Richard Canary, François Labourie
We show that a Hitchin representation is determined by the spectral radii of the images of simple, non-separating closed curves. As a consequence, we classify isometries of the int…
Windows, cores and skinning maps
Jeffrey F. Brock, Kenneth W. Bromberg, Richard D. Canary +1
We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrica…
Simple length rigidity for Kleinian surface groups and applications
Martin Bridgeman, Richard D. Canary
We prove that a Kleinian surface groups is determined, up to conjugacy in the isometry group of , by its simple marked length spectrum. As a first application, we show…
Amalgam Anosov representations
Richard D. Canary, Michelle Lee, Matthew Stover
Let be a one-ended, torsion-free hyperbolic group and let be a semisimple Lie group with finite center. Using the canonical JSJ splitting due to Sela, we define amalgam Ano…
Convergence and divergence of Kleinian surface groups
Jeffrey Brock, Kenneth Bromberg, Richard Canary +1
We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifo…
An improved bound for Sullivan's convex hull theorem
Martin Bridgeman, Richard Canary, Andrew Yarmola
Sullivan showed that there exists such that if is a simply connected hyperbolic domain, then there exists a conformally natural -quasiconform…
Dynamics on character varieties: a survey
Richard D. Canary
We survey recent work on the dynamics of the outer automorphism group of a word hyperbolic group on spaces of (conjugacy classes of) representations ofthe group into a semi-simple…
Convergence properties of end invariants
Jeffrey F. Brock, Kenneth W. Bromberg, Richard D. Canary +1
We prove a continuity property for ending invariants of convergent sequences of Kleinian surface groups. We also analyze the bounded curve sets of such groups and show that their p…
Dynamics on PSL(2,C)-character varieties: 3-manifolds with toroidal boundary components
Richard Canary, Aaron Magid
Let M be a compact, orientable, hyperbolizable 3-manifold with incompressible boundary which is not an interval bundle. We study the dynamics of the action of the outer automorphis…
Uniformly perfect domains and convex hulls
Martin Bridgeman, Richard Canary
Given a hyperbolic domain, the nearest point retraction is a conformally natural homotopy equivalence from the domain to the boundary of the convex core of its complement. Marden a…
Marden's Tameness Conjecture: history and applications
Richard D. Canary
Marden's Tameness Conjecture predicts that every hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold. It was rec…
The Thurston metric on hyperbolic domains and boundaries of convex hulls
Martin Bridgeman, Richard Canary
We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain in the Riemann sphere to the boundary of the convex hull of it…
Introductory bumponomics: the topology of deformation spaces of hyperbolic 3-manifolds
Richard D. Canary
We survey work on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with boundary. The interior of AH(M) is…
Local topology in deformation spaces of hyperbolic 3-manifolds
Jeffrey F. Brock, Kenneth W. Bromberg, Richard D. Canary +1
We prove that the deformation space AH(M) of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with incompressible boundary is locally connected at…
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties
Richard D. Canary, Peter A. Storm
The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a compact 3-manifold with boundary M sits inside the PSL_2(C)-character variety X(M) of π_1(M). We study the…
Kleinian groups with discrete length spectrum
Richard D. Canary, Christopher J. Leininger
We characterize finitely generated torsion-free Kleinian groups for which the real length spectrum (without multiplicities) is discrete.
The classification of Kleinian surface groups, II: The Ending Lamination Conjecture
Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky
Thurston's Ending Lamination Conjecture states that a hyperbolic 3-manifold N with finitely generated fundamental group is uniquely determined by its topological type and its end i…
Cores of hyperbolic 3-manifolds and limits of Kleinian groups II
James W. Anderson, Richard D. Canary
Troels Jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic Kleinian groups agree if there are no new parabolics in t…
The visual core of a hyperbolic 3-manifold
James W. Anderson, Richard D. Canary
We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the c…
Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds
Richard D. Canary, Yair N. Minsky, Edward C. Taylor
Let M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Lambda(M) be the supremum of the bottom eigenvalue of the Laplacian of N, where N varies…