Embedded disk on the complement ofo a simple closed geodesic.

Hugo Parlier

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Simple geodesics on surfaces of genus 2.

McShane, Greg (2006)

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Lengths of geodesics on Riemann surfaces with boundary.

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Length functions and parameterizations of Teichmüller space for surfaces with cusps.

Hämenstadt, Ursula (2003)

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Involutions and simple closed geodesics on Riemann surfaces.

Schmutz Schaller, Paul (2000)

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Continuity of the bending map

Cyril Lecuire (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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The bending map of a hyperbolic $3$ -manifold maps a convex cocompact hyperbolic metric on a $3$ -manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.