Mathematics

The main goal of the course is to provide a concise introduction to 4-manifold topology. A list of topics to be covered is as follows.

• Intersection forms of closed oriented 4-manifolds. 
• Freedman’s topological classification of closed simply connected 4-manifolds.
• Donaldson’s and Furuta's results on definite forms that can be realized as the intersection form of a closed smooth 4-manifold.
• Geography of symplectic 4-manifolds. 
• Homology classes represented by smoothly embedded surfaces and the genus function.