Simon's conjecture for fibered knots (2009)
The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being...
A fake Schottky group in Mod(S) (2009)
Kent IV, Richard P., Leininger, Christopher J.
We use the classical construction of Schottky groups in hyperbolic geometry to produce non-Schottky subgroups of the mapping class group.
Small dilatation pseudo-Anosovs and 3-manifolds (2009)
Farb, Benson, Leininger, Christopher J., Margalit, Dan
The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms, ranging over all surfaces. More precisely, we consider pseudo-Anosovs...
In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S 3 for which the complement contains a closed embedded totally geodesic surface. In this note, we show that...
Kleinian groups with discrete length spectrum (2008)
Richard D. Canary, Christopher J. Leininger
We characterize finitely generated torsion-free Kleinian groups whose real length spectrum (without multiplicities) is discrete.
Compressing totally geodesic surfaces (2008)
In this paper we prove that one can find surgeries arbitrarily close to infinity in the Dehn surgery space of the figure eight knot complement for which some immersed totally geodesic surface...
Two-generator subgroups of the pure braid group (2008)
Leininger, Christopher J, Margalit, Dan
We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group...
Compressing totally geodesic surfaces (2008)
Abstract In this paper we prove that one can find surgeries arbitrarily close to infinity in the Dehn surgery space of the figure eight knot complement for which some immersed totally geodesic...
Injections of mapping class groups (2008)
Aramayona, Javier, Leininger, Christopher J., Souto, Juan
We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The...
The universal Cannon--Thurston maps and the boundary of the curve complex (2008)
Leininger, Christopher J., Mj, Mahan, Schleimer, Saul
In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of...
A combination theorem for Veech subgroups of the mapping class group, Geom (2008)
Christopher J. Leininger, Alan W. Reid
In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups...
The lower central series and pseudo-Anosov dilatations (2008)
Benson Farb, Christopher J. Leininger, Dan Margalit
American Journal of Mathematics - Volume 130, Number 3, June 2008
Connectivity of the space of ending laminations (2008)
Leininger, Christopher J., Schleimer, Saul
We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E. Klarreich implies that this...
Connectivity of the space of ending laminations. (2008)
Christopher J. Leininger, Saul Schleimer
Abstract We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E. Klarreich implies...
Connectivity of the space of ending laminations. (2008)
Christopher J. Leininger, Saul Schleimer
We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E. Klarreich implies that this...
Kleinian groups with discrete length spectrum (2007)
Canary, Richard D., Leininger, Christopher J.
We characterize finitely generated torsion-free Kleinian groups whose real length spectrum (without multiplicities) is discrete.
Uniform convergence in the mapping class group (2007)
Kent IV, Richard P., Leininger, Christopher J
We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as...
Accidental parabolics in mapping class groups (2007)
In this note we discuss the behavior of the Gromov boundaries and limit sets for the surface subgroups of the mapping class group with accidental parabolics constructed by the author and A. Reid in...
Subgroups of the mapping class group from the geometrical viewpoint (2007)
Kent IV, Richard P., Leininger, Christopher J.
We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.
Shadows of mapping class groups:capturing convex cocompactness (2007)
for Dick and Geri 1 Introduction A Kleinian group \Gamma is a discrete subgroup of PSL2(C). When non-elementary, sucha group possesses a unique non-empty minimal closed invariant subset \Lambda...
Trees and mapping class groups (2007)
Christopher J. Leininger, Saul Schleimer
There is a forgetful map from the mapping class group of a punctured surface to that of the surface with one fewer puncture. We prove that finitely generated purely pseudo-Anosov subgroups of the...
Uniform convergence in the mapping class group (2007)
We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as...
Kleinian groups with discrete length spectrum (2007)
Canary, Richard D., Leininger, Christopher J.
We characterize finitely generated torsion-free Kleinian groups whose real length spectrum (without multiplicities) is discrete.
Kleinian groups with discrete length spectrum (2007)
Canary, Richard D., Leininger, Christopher J.
We characterize finitely generated torsion-free Kleinian groups whose real length spectrum (without multiplicities) is discrete.
Trees and mapping class groups (2006)
Kent IV, Richard P., Leininger, Christopher J., Schleimer, Saul
There is a forgetful map from the mapping class group of a punctured surface to that of the surface with one fewer puncture. We prove that finitely generated purely pseudo-Anosov subgroups of the...
Length and eigenvalue equivalence (2006)
Leininger, Christopher J., McReynolds, D. B., Neumann, Walter D., Reid, Alan W.
Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent...
The lower central series and pseudo-Anosov dilatations (2006)
Farb, Benson, Leininger, Christopher J., Margalit, Dan
The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface S_g of genus g. Penner proved that the logarithm of the minimal...
Separable subgroups of mapping class groups 1 Separable subgroups of mapping class groups (2006)
Christopher J. Leininger, D. B. Mcreynolds
We investigate separability questions for the mapping class group of a surface. While this group is not subgroup separable in general, we prove a large family of interesting subgroups are separable....
The lower central series and pseudo-Anosov dilatations, preprints (2006)
Benson Farb, Christopher J. Leininger, Dan Margalit
The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface Sg of genus g. Penner proved that the logarithm of the minimal...
Subgroups of mapping class groups from the geometrical viewpoint (2006)
Once it is possible to translate any particular proof from one theory to another, then the analogy has ceased to be productive for this purpose; it would cease to be at all productive if at one point...
Subgroups of mapping class groups from the geometrical viewpoint (2006)
Once it is possible to translate any particular proof from one theory to another, then theanalogy has ceased to be productive for this purpose; it would cease to be at all productive if at one point...
Kleinian groups with discrete length spectrum (2005)
Canary, Richard D., Leininger, Christopher J.
We characterize finitely generated torsion-free Kleinian groups for which the real length spectrum (without multiplicities) is discrete.
Separable subgroups of mapping class groups (2005)
Leininger, Christopher J., McReynolds, D. B.
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
Shadows of mapping class groups: capturing convex cocompactness (2005)
Kent IV, Richard P., Leininger, Christopher J.
We strengthen the analogy between convex co-compact Kleinian groups and convex co-compact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).
Abstract commensurators of braid groups (2005)
Leininger, Christopher J., Margalit, Dan
Let B_n be the braid group on n strands, with n at least 4, and let Mod(S) be the extended mapping class group of the sphere with n+1 punctures. We show that the abstract commensurator of B_n is...
A combination theorem for Veech subgroups of the mapping class group (2004)
Leininger, Christopher J., Reid, Alan W.
In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups...
Small curvature surfaces in hyperbolic 3-manifolds (2004)
In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S^3 for which the complement contains a closed embedded totally geodesic surface. In this note, we show that...
T T Tttt, Christopher J Leininger
On groups generated by two positive multi-twists: Teichmüller curves and Lehmer’s number
On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number (2003)
From a simple observation about a construction of Thurston, we derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists. In particular, we...
Equivalent curves in surfaces (2003)
We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to...
Equivalent curves in surfaces (2003)
1 Introduction Given a closed orientable surface S of genus g> 1, there exists distinct homotopy classes of curves fl and fl0 on S such that lengthX(fl) = lengthX(fl0)
Equivalent curves in surfaces (2003)
Given a closed orientable surface S of genus g> 1, there exists distinct homotopy classes of curves
The co-rank conjecture for 3-manifold groups (2002)
Leininger, Christopher J., Reid, Alan W.
In this paper we construct explicit examples of both closed and non-compact finite volume hyperbolic manifolds which provide counterexamples to the conjecture that the co-rank of a 3-manifold group...
The co-rank conjecture for 3-manifold groups (2002)
Christopher J. Leininger, Alan W. Reid
Abstract In this paper we construct explicit examples of both closed and non-compact finite volume hyperbolic manifolds which provide counterexamples to the conjecture that the co-rank of a...
Surgeries on one component of the Whitehead link are virtually fibered, Topology 41 (2002)
In this paper we will show that every Dehn filling on one component of the boundary of the exterior of the Whitehead link is virtually fibered. As a corollary we produce what seem to be the first...
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