[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.