Related papers: Pleating coordinates for the Teichm\"{u}ller space…

Over the past two decades the theory of the Weil-Petersson metric has been extended to general Teichm\"uller spaces of infinite type, including for example the universal Teichm\"uller space. In this paper we give a survey of the main…

This paper is a comprehensive introduction to the results of [7]. It grew as an expanded version of a talk given at INdAM Meeting Complex and Symplectic Geometry, held at Cortona in June 12-18, 2016. It deals with the construction of the…

We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the Teichm\"uller metric is approximated up…

Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on S was first defined and topologized by the first author. In this article, we give an explicit…

Let $X_0$ be an infinite genus hyperbolic surface (whose boundary components, if any, are closed geodesics or punctures) which has an upper bounded pants decomposition. The length spectrum Teichm\"uller space $T_{ls}(X_0)$ consists of all…

Grafting is a method of obtaining new projective structures from a hyperbolic structure, basically by gluing a flat cylinder into a surface along a closed geodesic in the hyperbolic structure, or by limits of that procedure. This induces a…

We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces in terms of natural and effective coordinates as the space of certain (2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We essentially…

In [4]: `The Riley slice of Schottky space', (Proc. London Math. Soc. 69 (1994), 72-90), Keen and Series analysed the theory of pleating coordinates in the context of the Riley slice of Schottky space R, the deformation space of a genus two…

We show that any grafting ray in Teichm\"{u}ller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichm\"{u}ller geodesic ray. As a consequence the projection of a generic grafting ray to moduli…

We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell…

One of the basic geometric objects in conformal field theory (CFT) is the the moduli space of Riemann surfaces whose $n$ boundaries are ''rigged'' with analytic parametrizations. The fundamental operation is the sewing of such surfaces…

We study Thurston's Lipschitz and curve metrics, as well as the arc metric on the Teichmueller space of one-hold tori equipped with complete hyperbolic metrics with boundary holonomy of fixed length. We construct natural Lipschitz maps…

We define new coordinates for Fock-Goncharov's higher Teichm\"uller spaces for a surface with holes, which are the moduli spaces of representations of the fundamental group into a reductive Lie group $G$. Some additional data on the…

The universal Teichm\"uller space is an infinitely dimensional generalization of the classical Teichm\"uller space of Riemann surfaces. It carries a natural Hilbert structure, on which one can define a natural Riemannian metric, the…

Quantum Teichmuller theory assigns invariants to three-manifolds via projective representations of mapping class groups derived from the representation of a noncommutative torus. Here, we focus on a representation of the simplest…

We study the geometry of exceptional loci of birational contractions of hyper-K\"ahler fourfolds that are of K3$^{[2]}$-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use…

We study the geometry of the Thurston metric on the Teichm\"uller space $\mathcal{T}(S)$ of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type;…

We define the quantum correction of the Teichm\"uller space $\mathcal{T}$ of Calabi-Yau manifolds. Under the assumption of no weak quantum correction, we prove that the Teichm\"uller space $\mathcal{T}$ is a locally symmetric space with the…

Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the natural action of the group of volume-preserving…

Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichm\"uller spaces. We show that for dimension at least $2$, all isometric embeddings arise from branched coverings. This generalizes a…