[Geometry, Topology and Dynamics Seminar] Neck-pinching of CP^1-structures by Dr. Shinpei Baba (Osaka University)
Abstract: A CP^1-structure is a geometric structure on a (compact oriented) surface S and its holonomy is a homomorphism from the fundamental group of the surface into PSL(2, C). Moreover it corresponds to a holomorphic quadratic differential on a Riemann surface.
We consider a path C_t of CP^1-structures on S such that C_t diverges to infinity in its deformation space and yet its holonomy converges. We describe its asymptotic behavior of C_t under the assumption the Riemann surface structure on C_t is pinched along a single loop.