Kentaro ITO

Exotic projective structures and boundary of quasi-Fuchsian space


Let P(S) denote the space of projective structures on a closed surface S. It is known that the subset Q(S) of projective structures P(S) with quasi-Fuchsian holonomy has infinitely many connected components. In this paper, we investigate the configuration of these components. In particular, we show that the closure of any exotic component of Q(S) intersects the closure of the standard component of Q(S). As a consequence, Q(S) has connected closure in P(S). We also mention the complexity of the boundary of the quasi-Fuchsian space.

submission: October 10, 1999
revision: October 22, 1999

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