Continuity of the bending map

Details Continuity of the bending map Continuity of the bending map

2004-11-18

arxiv.org/abs/math/0411412v1

Mathematics

Differential Geometry

17 pages, 2 figures. Available also at http://www.maths.warwicK.ac.uk/~clecuire

Scientific paper

The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. 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 shows that the quotient map obtained from the bending map is continuous.

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