Configuration spaces of points on the circle and hyperbolic Dehn fillings

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

1998-09-25

arxiv.org/abs/math/9809147v1

Topology, 38 (1999), 497-516.

Mathematics

Geometric Topology

22 pages, to appear in Topology

Scientific paper

A purely combinatorial compactification of the configuration space of n (>4) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n-3. Then, we vary weights for points. The geometrization still makes sense and yields a deformation. The effectivity of deformations arisen in this manner will be locally described in the existing deformation theory of hyperbolic structures when n-3 = 2, 3.

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