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Equivalent Curves in Surfaces

- C. Leininger
- Mathematics
- 23 February 2003

We consider various notions of equivalence for homotopy classes of curves on hyperbolic surfaces based on topological, algebraic, and geometric structures, and find the relationships between these… Expand

Length spectra and degeneration of flat metrics

- M. Duchin, C. Leininger, Kasra Rafi
- Mathematics
- 13 July 2009

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves… Expand

FINITE RIGID SETS IN CURVE COMPLEXES

- J. Aramayona, C. Leininger
- Mathematics
- 14 June 2012

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex 𝔛 of the curve complex such that every… Expand

On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number

- C. Leininger
- Mathematics
- 14 April 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… Expand

Shadows Of Mapping Class Groups: Capturing Convex Cocompactness

- Richard P. Kent, C. Leininger
- Mathematics
- 6 May 2005

Abstract.We strengthen the analogy between convex cocompact Kleinian groups and convex cocompact subgroups of the mapping class group of a surface in the sense of B. Farb and L. Mosher.

The geometry of right angled Artin subgroups of mapping class groups

- Matt Clay, C. Leininger, J. Mangahas
- Mathematics
- 7 July 2010

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under… Expand

Small dilatation pseudo-Anosovs and 3-manifolds

- Benson Farb, C. Leininger, D. Margalit
- Mathematics
- 2 May 2009

The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms φ : S → S, ranging over all surfaces S. More precisely, we consider… Expand

On the number and location of short geodesics in moduli space

- C. Leininger, D. Margalit
- Mathematics
- 28 October 2011

A closed Teichmüller geodesic in the moduli space ℳg of Riemann surfaces of genus g is called L‐short if it has length at most L/g. We show that, for any L>0, there exist R>ϵ>0, independent of g, so… Expand

Exhausting curve complexes by finite rigid sets

- J. Aramayona, C. Leininger
- Mathematics
- 21 October 2014

Let $S$ be a connected orientable surface of finite topological type. We prove that there is an exhaustion of the curve complex $\mathcal{C}(S)$ by a sequence of finite rigid sets.

Pseudo‐Anosov stretch factors and homology of mapping tori

- I. Agol, C. Leininger, D. Margalit
- MathematicsJ. Lond. Math. Soc.
- 24 September 2014

We consider the pseudo‐Anosov elements of the mapping class group of a surface of genus g that fix a rank k subgroup of the first homology of the surface. We show that the smallest entropy among… Expand

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