Configuration spaces of points on the circle and hyperbolic Dehn fillings, II

Details Configuration spaces of points on the circle and hyperbolic Dehn fillings, II Configuration spaces of points on the circle and hyperbolic Dehn fillings, II

1999-07-24

arxiv.org/abs/math/9907163v1

Geometriae Dedicata 89 (2002) 143-157

Mathematics

Geometric Topology

14 pages, 14 figures

Scientific paper

10.1023/A:1014220417320

In our previous paper, we discussed the hyperbolization of the configuration space of n(> 4) marked points with weights in the projective line up to projective transformations. A variation of the weights induces a deformation. It was shown that this correspondence of the set of the weights to the Teichm\"uller space when n = 5 and to the Dehn filling space when n= 6 is locally one-to-one near the equal weight. In this paper, we establish its global injectivity.

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