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Complex projective structures with Fuchsian Holonomy
Student-Run Geometry/Topology| Speaker: | Shinpei Baba, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, Nov 27 2007, 12:00AM |
Description
Complex projective structure is structure on a closed orientable
surface, which is a generalization of hyperbolic structure.
Every discrete and faithful representation from the surface group to
PSL(2,R) corresponds to a unique complete hyperbolic structure.
On the other hand, every representation from the surface group to PSL(2,C)
with some much milder conditions corresponds to infinitely many complex
projective structures.
In the case that the representation is an isomorphism onto a quasifuchsian
group, its corresponding complex projective structures are beautifully
characterized by William Goldman, and his key argument uses bundles and
Euler classes.
I will give another proof of the characterization theorem using only
hyperbolic geometry techniques.