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

Literature:

- 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)