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CP^1-structures on surfaces and representations of surface groups into PSL(2, C)

Shinpei Baba (Universität Heidelberg)
Fredag, 20 maj, 2016, at 14:15-15:15, in Aud. G1 (1532-116)
We consider certain geometric structure (locally homogeneous structure) on a surface, called CP^1-structure. CP^1-structures are related to different areas such as ordinary differential equations, Riemann surfaces, hyperbolic geometry, and representations of surface groups. Indeed the holonomy representation of every CP^1-structure is a homomorphism from the fundamental group of the surface into PSL(2, C). We discuss the relation between the deformation space of CP^1-structures on a surface and the space of such representations. In particular, I explain about a (2pi-)grafting operation, which creates different CP^1-structures having the same holonomy representation.

Note: This talk is aimed at a general audience of mathematicians.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen