Kobayashi’s metric on Teichmüller space

1999 ◽  
pp. 145-154
Author(s):  
Frederick Gardiner ◽  
Nikola Lakic
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space

scholarly journals Pleating coordinates for the maskit embedding of the teichmüller space of punctured tori

Topology ◽  
1993 ◽  
Vol 32 (4) ◽  
pp. 719-749 ◽  
Author(s):  
Linda Keen ◽  
Caroline Series
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space

scholarly journals The skein algebra of arcs and links and the decorated Teichmüller space

2014 ◽  
Vol 96 (1) ◽  
pp. 95-140 ◽  
Author(s):  
Julien Roger ◽  
Tian Yang
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space

NEW POLARIZATIONS ON THE MODULI SPACES AND THE THURSTON COMPACTIFICATION OF TEICHMÜLLER SPACE

1998 ◽  
Vol 09 (01) ◽  
pp. 1-45 ◽  
Author(s):  
JØRGEN ELLEGAARD ANDERSEN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Teichmüller Space ◽  
Closed Surface ◽  
Teichmuller Space ◽  
Open Dense Subset ◽  
Complex Structures ◽  
Thurston Boundary ◽  
Simply Connected ◽  
Singular Metric

Given a foliation F with closed leaves and with certain kinds of singularities on an oriented closed surface Σ, we construct in this paper an isotropic foliation on ℳ(Σ), the moduli space of flat G-connections, for G any compact simple simply connected Lie-group. We describe the infinitesimal structure of this isotropic foliation in terms of the basic cohomology with twisted coefficients of F. For any pair (F, g), where g is a singular metric on Σ compatible with F, we construct a new polarization on the symplectic manifold ℳ′(Σ), the open dense subset of smooth points of ℳ(Σ). We construct a sequence of complex structures on Σ, such that the corresponding complex structures on ℳ′(Σ) converges to the polarization associated to (F, g). In particular we see that the Jeffrey–Weitzman polarization on the SU(2)-moduli space is the limit of a sequence of complex structures induced from a degenerating family of complex structures on Σ, which converges to a point in the Thurston boundary of Teichmüller space of Σ. As a corollary of the above constructions, we establish a certain discontinuiuty at the Thurston boundary of Teichmüller space for the map from Teichmüller space to the space of polarizations on ℳ′(Σ). For any reducible finite order diffeomorphism of the surface, our constuction produces an invariant polarization on the moduli space.

scholarly journals Convergence of earthquake and horocycle paths to the boundary of Teichmüller space

2016 ◽  
Vol 59 (10) ◽  
pp. 1937-1948
Author(s):  
ManMan Jiang ◽  
WeiXu Su
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space
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