Kentaro ITO
Exotic projective structures and boundary of quasi-Fuchsian space
Abstract
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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