Stockholm university
Gå till denna sida på svenska webben

Algebraic Topology

Learn to state and prove basic theorems in algebraic topology, and compute the (co)homology of topological spaces and interpret the results geometrically.

The course covers:

  • singular homology and cohomology of topological spaces
  • exact sequences, chain complexes and homology
  • homotopy invariance of singular homology
  • the Mayer-Vietoris sequence and excision
  • cell complexes and cellular homology
  • the cohomology ring
  • homology and cohomology of spheres and projective spaces
  • applications such as the Brouwer Fixed Point theorem, the Borsuk-Ulam theorem and theorems about vectorfields on spheres

This course is given jointly by Stockholm University and KTH, and can be a part of the Master's Programme in Mathematics but may also be taken as a separate course.