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On FenchelNielsen coordinates on Teichmüller spaces of surfaces of infinite type
, 2010
"... We introduce FenchelNielsen coordinates on Teichmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type ca ..."
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Cited by 11 (6 self)
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We introduce FenchelNielsen coordinates on Teichmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geometric decomposition, that is, a decomposition into hyperbolic pairs of pants. This is expressed in terms of a condition we introduce and which we call Nielsen convexity. This condition is related to Nielsen cores of Fuchsian groups. We use this to define the FenchelNielsen Teichmüller space associated to a geometric pair of pants decomposition. We study a metric on such a Teichmüller space, and we compare it to the quasiconformal Teichmüller space, equipped with the Teichmüller metric. We study conditions under which there is an equality between these Teichmüller spaces and we study topological and metric properties of the identity map when this map exists.
SOME METRICS ON TEICHMÜLLER SPACES OF SURFACES OF INFINITE TYPE
, 2009
"... Unlike the case of surfaces of topologically finite type, there are several different Teichmüller spaces that are associated to a surface of topological infinite type. These Teichmüller spaces first depend (settheoretically) on whether we work in the hyperbolic category or in the conformal catego ..."
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Cited by 8 (7 self)
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Unlike the case of surfaces of topologically finite type, there are several different Teichmüller spaces that are associated to a surface of topological infinite type. These Teichmüller spaces first depend (settheoretically) on whether we work in the hyperbolic category or in the conformal category. They also depend, given the choice of a point of view (hyperbolic or conformal), on the choice of a distance function on Teichmüller space. Examples of distance functions that appear naturally in the hyperbolic setting are the length spectrum distance and the biLipschitz distance, and there are other useful distance functions. The Teichmüller spaces also depend on the choice of a basepoint. The aim of this paper is to present some examples, results and questions on the Teichmüller theory of surfaces of infinite topological type that do not appear in the setting the Teichmüller theory of surfaces of finite type. In particular, we point out relations and differences between the various Teichmüller spaces associated to a given surface of topological infinite type.
On various Teichmüller spaces of a surface of infinite topological type
 Proc. Amer. Math. Soc. 140 (2012), 561–574. SPACE 19 hal00664093, version 1  28
, 2012
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On local comparison between various metrics on Teichmüller spaces
, 2011
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On the inclusion of the quasiconformal Teichmüller space into the lengthspectrum Teichmüller space
, 2012
"... Given a surface of infinite topological type, there are several Teichmüller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the comparison between the quasiconformal Teichmüller space and the ..."
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Cited by 3 (1 self)
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Given a surface of infinite topological type, there are several Teichmüller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the comparison between the quasiconformal Teichmüller space and the lengthspectrum Teichmüller space. We work under this hypothesis that the basepoint is upperbounded and admits short interior curves. There is a natural inclusion of the quasiconformal space in the lengthspectrum space. We prove that, under the above hypothesis, the image of this inclusion is nowhere dense in the lengthspectrum space. As a corollary we find an explicit description of the lengthspectrum Teichmüller space in terms of FenchelNielsen coordinates and we prove that the lengthspectrum Teichmüller space is pathconnected.