Related papers: Noded Teichmueller spaces

Let ${\cal M}_{g,n}$ and ${\cal H}_{g,n}$, for $2g-2+n>0$, be, respectively, the moduli stack of $n$-pointed, genus $g$ smooth curves and its closed substack consisting of hyperelliptic curves. Their topological fundamental groups can be…

Let G be a split semisimple algebraic group with trivial center. Let S be a compact oriented surface, with or without boundary. We define {\it positive} representations of the fundamental group of S to G(R), construct explicitly all…

In this paper we prove that for all $n=4k-2$, $k\ge2$ there exists closed $n$-dimensional Riemannian manifolds $M$ with negative sectional curvature that do not have the homotopy type of a locally symmetric space, such that…

In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant Cheeger-M\"{u}ller theorem simplifies considerably when applied to locally symmetric spaces. In a…

We present an outline of the theory of universal Teichmuller space, viewed as part of the theory of QS, the space of quasisymmetric homeomorphisms of a circle. Although elements of QS act in one dimension, most results depend on a…

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…

We will develop a formal non-commutative (NC) deformation theory of smooth algebraic varieties $X$ defined over a field $k$, and describe a semi-universal deformation where the tangent space $T^1$ and the obstruction space $T^2$ are given…

Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichm\"uller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the…

Let $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\delta (T)$ the number of non isomorphic indecomposable summands of $T$.…

We generalize a new class of cluster type mutations for which exchange transformations are given by reciprocal polynomials. In the case of second-order polynomials of the form $x+2\cos{\pi/n_o}+x^{-1}$ these transformations are related to…

The paper presents some recent results on the Weil-Petersson geometry theory of the universal Teichm\"uller space, a topic which is important in Teichm\"uller theory and has wide applications to various areas such as mathematical physics,…

We show that any element of the universal Teichm\"uller space is realized by a unique minimal Lagrangian diffeomorphism from the hyperbolic plane to itself. The proof uses maximal surfaces in the 3-dimensional anti-de Sitter space. We show…

We show that if Teichm\"uller geodesics spend enough time in the thick part of moduli space, they display CAT(-1)-type properties. In particular, they exponentially contract along strongly stable leaves. As an application we prove two…

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The…

Let S be an oriented surface of genus g with m punctures. If 3g-3+m is at least 4 then we construct for every compact subset K of moduli space a closed Teichmueller geodesic not intersecting K.

Let $K$ be a field and $G$ be a group of its automorphisms endowed with the compact-open topology. There are many situations, where it is natural to study the category $Sm_K(G)$ of smooth (i.e. with open stabilizers) $K$-semilinear…

Let $\gamma$ be a pseudo-Anosov homeomorphism and $X$ an element of the Teichmuller space of a genus $g$ surface. In this paper, we find asymptotics for the number of pseudo-Anosov homeomorphisms that are conjugate to $\gamma$ and the axis…

Let $G$ be a locally compact amenable group, $TLIM(G)$ the topological left-invariant means on $G$, and $TLIM_0(G)$ the limit points of Folner-nets. I show that $TLIM_0(G) = TLIM(G)$ unless $G$ is $\sigma$-compact non-unimodular, in which…

In this paper we study the Goldman bracket between geodesic length functions both on a Riemann surface $\Sigma_{g,s,0}$ of genus $g$ with $s=1,2$ holes and on a Riemann sphere $\Sigma_{0,1,n}$ with one hole and $n$ orbifold points of order…

We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds $\mathcal{O}$, the Teichm\"uller space of flat metrics $\mathcal{T}_{\text{flat}}(\mathcal{O})$ serves as a…