Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 32, 2007, 3-12

THE INTERIOR OF DISCRETE PROJECTIVE STRUCTURES IN THE BERS FIBER

Katsuhiko Matsuzaki

Department of Mathematics, Okayama University
Tsushima-Naka 3-1-1, Okayama 700-8530, Japan; matsuzak 'at' math.okayama-u.ac.jp

Abstract. The space of all projective structures on a closed surface is a holomorphic vector bundle over the TeichmŘller space. In this paper, we restrict the space to the Bers fiber over any fixed underlying complex structure and prove that the interior of the set of discrete projective structures in the Bers fiber consists of those having quasifuchsian holonomy.

2000 Mathematics Subject Classification: Primary 30F40.

Key words: Projective structure, holonomy representation, Kleinian group, quasifuchsian group, degenerate group, grafting, Bers density conjecture.

Reference to this article: K. Matsuzaki: The interior of discrete projective structures in the Bers fiber. Ann. Acad. Sci. Fenn. Math. 32 (2007), 3-12.

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