UvA Algebraic and Differential Topology, First semester 2003

Course on Algebraic and Differential Topology Vaknaam: Algebraic and Differential Topology
Target group: master Mathematics
Semester: 1
Teaching method: lecture and practical work
Credits: 6-8
Examination: term paper

Prior knowledge:
- basics of point set topology,
- basics of manifolds and differential forms,
- fundamental group and covering spaces (desirable but not crucial)

Content: (more details will be given later)
- basic differential topology: Sard's theorem, transversality...
- algebraic topology of manifolds: de Rham cohomology, orientation, Poincare duality...
- basics of Morse theory, Morse inequalities, Morse homology

- G. E. Bredon: Topology and geometry
- R. Bott, L. Tu: Differential forms in algebraic topology
- V. Guillemin, A. Pollack: Differential topology
- M. Hirsch: Differential topology
- J. Jost: Riemannian geometry and geometric analysis (Chapter 6)

Introduction to differential topology, de Rham theory and Morse theory (Latest Version: 04.04.05) (pdf file)

Survey article by Martin Guest on Morse theory (pdf file)