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      Combination of affine deformations on a hyperbolic surface

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          Abstract

          This paper is a continuation of the previous paper of the author[M]. We show that an affine deformation space of a hyperbolic surface of type (g,b) can be parametrized by Margulis invariants and affine twist parameters with a certain decomposition of the surface, which are associated with the Fenchel-Nielsen coordinates in Teichmuller theory. W.Goldman and G.Margulis[GM] introduced that a translation part of an affine deformation canonically corresponds to a tangent vector on the Teichmuller space. By this correspondence, we explicitly represent tangent vectors on the Teichmuller space from the perspective of Lorentzian geometry, only when the tangent vectors correspond to Fenchel-Nielsen twists along separating geodesic curves on a hyperbolic surface.

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          Most cited references 7

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          Margulis spacetimes via the arc complex

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            An elementary formula for the Fenchel-Nielsen twist

             Scott Wolpert (1981)
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              Affine deformations of a three-holed sphere

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                Author and article information

                Journal
                2016-06-20
                Article
                1606.05966

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                51H20
                16 pages
                math.GT

                Geometry & Topology

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