MA342R Hilary Term 2017 - Provisional Course Outline

• Basic Results concerning Topological Spaces (4 lectures?)
• Winding Numbers and Monodromy
• Fundamental Groups of Topological Spaces
• Covering Maps
• Discontinuous Group Actions (?)

Study Week

• Topology and geometry of surfaces (possibly including the Gauss-Bonnet Theorem and/or the two-dimensional case of the Poincaré-Hopf Theorem
• Topological Classification of Closed Surfaces
• Further examples?