Mathematics

This is an introductory course on 4-manifold topology. Its purpose is to provide general knowledge to students working in related research areas like algebraic and complex geometry.  

• Topics:

1. Representing homology classes by embedded submanifolds.
2. Cobordisms and basic topological invariants.
3. Intersection form of a 4-manifold and classification up to homeomorphism.
4. Examples of non-smoothable 4-manifolds.
5. Smooth structures on R^4

• Bibliography:

1. Hirsch, Differential topology. 
2. Gompf-Stipsicz, 4-manifolds and Kirby calculus
3. Kirby, The topology of 4-manifolds.