Kentaro Ito

Exotic projective structures and quasi-fuchsian space

Abstract:

Let $P(S)$ denote the space of projective structures on a closed surface $S$. It is known that the subset $Q(S) \subset P(S)$ of projective structures with quasi-Fuchsian holonomy has infinitely many connected components; one is called standerd, the others are exotic. Here, we investigate the configuration of these components. In our previous paper (Duke Math. J. {\bf 105} (2000), 185--209), we showed that the closure of any exotic component intersects the closure of the standard component. We develop our argument there and show that any two components have intersecting closures.