Geometric Structures on surfaces and Teichmuller Space (MAGIC028)
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Classification of compact Riemann surfaces. Complex and geometric structures on compact surfaces. Teichmüller space. Coordinates on Teichmüller space.
Spring 2017 (Monday, January 23 to Friday, March 31)
Basic point set topology
The hyperbolic plane and hyperbolic geometry Complex and hyperbolic structures on surfaces Covering space theory for manifolds with extra structure Uniformising theorems for simply connected surfaces with complex or hyperbolic structure. Groups of holomorphic bijections. Covering groups of surfaces. More on hyperbolic geometry. Geodesics, perpendiculars, polygons. Hyperbolic structures on pairs of pants and compact surfaces with boundary. Isotopy of loops and homeomorphisms. Ambient isotopy. Mapping class groups. Teichmuller space. Coordinates, topology.
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Assessment will be by a take-home examination in the examination period 24 April -7 May. The examination will be available for viewing and download on 24 April. It will be designed to completed in two hours by a student who has engaged with the course.
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