Mathematics Colloquia and Seminars
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Complex projective structures with Schottky holonomyGeometry/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.