Topology 1
3-4 hours of lectures per week.
Lecturers:
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.