AdS manifolds with particles and earthquakes on singular surfaces

Francesco Bonsante; Jean-Marc Schlenker

AdS manifolds with particles and earthquakes on singular surfaces

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arxiv math/0609116 v2 pith:DQKKWV3F submitted 2006-09-04 math.GT math.DG

AdS manifolds with particles and earthquakes on singular surfaces

Francesco Bonsante , Jean-Marc Schlenker This is my paper

classification math.GT math.DG

keywords conesingularitiesangleearthquakehyperbolicmanifoldsparticlesspace

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We prove two related results. The first is an ``Earthquake Theorem'' for closed hyperbolic surfaces with cone singularities where the total angle is less than $\pi$: any two such metrics in are connected by a unique left earthquake. The second result is that the space of ``globally hyperbolic'' AdS manifolds with ``particles'' -- cone singularities (of given angle) along time-like lines -- is parametrized by the product of two copies of the Teichm\"uller space with some marked points (corresponding to the cone singularities). The two statements are proved together.

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