3-4 hours of lectures per week.
- Lecturer:
- Ib Madsen
- Content:
- Introduction to algebraic topology, with an emphasis on differential forms and de Rham cohomology groups. The following subjects will be treated:
- The alternating algebra and wedge product
- Differential forms and the de Rham complex
- Chain complexes and their cohomology
- Categories and functors
- Mayer-Vietoris sequences
- Homotopies
- Brouwers fixed point theorem
- Vector fields
- Jordan-Brouwers separation theorem
- Manifolds
- Integration on manifolds
- Stokes theorem
- Prerequisites:
- Elementary analysis and linear algebra. Some experiences with surfaces will help
- Literature:
- Ib Madsen and Jørgen Tornehave, "From Calculus to Cohomology", Cambridge Univ. Press, 1997.