Geometry, Topology and Dynamics Seminar
Shinpei Baba
UC Davis
Complex projective structures with Schottky holonomy
Abstract: A Schottky group in PSL(2,C) induces an open hyperbolic handlebody and its ideal boundary is a closed orientable surface $S$
whose genus is equal to the rank of the Schottky group. The boundary surface is equipped with a complex projective structure
and its holonomy representation is an epimorphism from $\pi_1(S)$ to the Schottky group. We show that an arbitrary projective
structure with the same holonomy representation is obtained by grafting the basic structure described above.
This result is an analogue to the characterization of the projective structures whose holonomy representation is an isomorphism
from $\pi_1(S)$ to a fixed quasifuchsian group, which was given by Goldman in 1987.
Monday September 22, 2008 at 3:00 PM in SEO 612