# Mathematics Colloquia and Seminars

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### Complex projective structures with Schottky holonomy

Geometry/Topology

 Speaker: Shinpei Baba, UC Davis Location: 2112 MSB Start time: Tue, Nov 25 2008, 4:10PM

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. This 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 will show that an arbitrary projective structure with the same holonomy representation is obtained by (2\pi-)grafting the basic structure described above. This result is an analog 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.