Exotic projective structures and quasifuchsian spaces II

Details Exotic projective structures and quasifuchsian spaces II Exotic projective structures and quasifuchsian spaces II

2006-03-03

arxiv.org/abs/math/0603074v1

Duke Math. J. Volume 140, Number 1 (2007), 85-109

Mathematics

Geometric Topology

22 pages, 9 figures

Scientific paper

10.1215/S0012-7094-07-14013-4

Let $P(S)$ be the space of projective structures on a closed surface $S$ of genus $g >1$ and let $Q(S)$ be the subset of $P(S)$ of projective structures with quasifuchsian holonomy. It is known that $Q(S)$ consists of infinitely many connected components. In this paper, we will show that the closure of any exotic component of $Q(S)$ is not a topological manifold with boundary and that any two components of $Q(S)$ have intersecting closures.

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