scholarly journals On ClusterC⁎-Algebras

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Igor V. Nikolaev
Keyword(s):  
Riemann Surface ◽  
Finite Number ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Generic Subset

We introduce aC⁎-algebraA(x,Q)attached to the clusterxand a quiverQ. IfQTis the quiver coming from triangulationTof the Riemann surfaceSwith a finite number of cusps, we prove that the primitive spectrum ofA(x,QT)timesRis homeomorphic to a generic subset of the Teichmüller space of surfaceS. We conclude with an analog of the Tomita-Takesaki theory and the Connes invariantT(M)for the algebraA(x,QT).

scholarly journals Harmonic maps and wild Teichmüller spaces

2019 ◽  
pp. 1-45
Author(s):  
Subhojoy Gupta
Keyword(s):  
Riemann Surface ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Teichmüller Space ◽  
Closed Surface ◽  
Hyperbolic Surface ◽  
Teichmuller Space ◽  
Quadratic Differentials ◽  
Hopf Differential ◽  
Principal Parts

We use meromorphic quadratic differentials with higher order poles to parametrize the Teichmüller space of crowned hyperbolic surfaces. Such a surface is obtained on uniformizing a compact Riemann surface with marked points on its boundary components, and has noncompact ends with boundary cusps. This extends Wolf’s parametrization of the Teichmüller space of a closed surface using holomorphic quadratic differentials. Our proof involves showing the existence of a harmonic map from a punctured Riemann surface to a crowned hyperbolic surface, with prescribed principal parts of its Hopf differential which determine the geometry of the map near the punctures.

scholarly journals On boundaries of Schottky spaces

1976 ◽  
Vol 62 ◽  
pp. 97-124 ◽  
Author(s):  
Hiroki Sato
Keyword(s):  
Riemann Surface ◽  
Half Plane ◽  
Fuchsian Group ◽  
Compact Riemann Surface ◽  
Teichmüller Space ◽  
Schottky Group ◽  
Teichmuller Space ◽  
Upper Half Plane

Let S be a compact Riemann surface and let Sn be the surface obtained from S in the course of a pinching deformation. We denote by Γn the quasi-Fuchsian group representing Sn in the Teichmüller space T(Γ), where Γ is a Fuchsian group with U/Γ = S (U: the upper half plane). Then in the previous paper [7] we showed that the limit of the sequence of Γn is a cusp on the boundary ∂T(Γ). In this paper we will consider the case of Schottky space . Let Gn be a Schottky group with Ω(Gn)/Gn = Sn. Then the purpose of this paper is to show what the limit of Gn is.

scholarly journals The geometry of measured geodesic laminations and measured train tracks

1989 ◽  
Vol 9 (3) ◽  
pp. 587-604 ◽  
Author(s):  
Howard Weiss
Keyword(s):  
Riemann Surface ◽  
Linear Model ◽  
Tangent Space ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Hölder Continuous ◽  
Geodesic Laminations ◽  
Non Linear ◽  
Train Tracks ◽  
Hyperbolic Riemann Surface

AbstractThurston and Kerckhoff have shown that the space of measured geodesic laminations on a hyperbolic Riemann surface serves as a non-linear model of the tangent space to Teichmüller space at the surface. In this paper we show that the natural map between these manifolds has stronger than Hölder continuous regularity.

scholarly journals ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS

2010 ◽  
Vol 52 (3) ◽  
pp. 593-604
Author(s):  
C. ZHANG
Keyword(s):  
Riemann Surface ◽  
Mapping Class Group ◽  
Isometric Embedding ◽  
Class Group ◽  
Teichmüller Space ◽  
Mapping Class Groups ◽  
Natural Projection ◽  
Mapping Class ◽  
Teichmuller Space ◽  
Class Groups

AbstractWe prove that for each Riemann surface of finite analytic type (p, n) with p ≥ 2, there exist uncountably many Teichmüller disks Δ in the Teichmüller space T(S), where S = - {a point a}, with these properties: (1) the natural projection j: T(S) → T() defined by forgetting a induces an isometric embedding of each Δ into T(); and (2) the stabilizer of each Teichmüller disk Δ in the a-pointed mapping class group of S is trivial.

A characterization of biholomorphic automorphisms of Teichmüller space

2012 ◽  
Vol 154 (1) ◽  
pp. 71-83
Author(s):  
RYOSUKE MINEYAMA ◽  
HIDEKI MIYACHI
Keyword(s):  
Riemann Surface ◽  
Finite Type ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Alternative Approach

AbstractIn this paper, we give an alternative approach to Royden–Earle–Kra–Markovic's characterization of biholomorphic automorphisms of Teichmüller space of Riemann surface of analytically finite type.

scholarly journals On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yan Wu ◽  
Yi Qi ◽  
Zunwei Fu
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Dual Space ◽  
Teichmüller Space ◽  
Geodesic Segment ◽  
Teichmuller Space ◽  
Quadratic Differentials ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Infinite Type

LetAZ(R)be the infinitesimal asymptotic Teichmüller space of a Riemann surfaceRof infinite type. It is known thatAZ(R)is the quotient Banach space of the infinitesimal Teichmüller spaceZ(R), whereZ(R)is the dual space of integrable quadratic differentials. The purpose of this paper is to study the nonuniqueness of geodesic segment joining two points inAZ(R). We prove that there exist infinitely many geodesic segments between the basepoint and every nonsubstantial point in the universal infinitesimal asymptotic Teichmüller spaceAZ(D)by constructing a special degenerating sequence.

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