Mathematics MA, Differential Topology

Education facts

Code: MA035A

The course provides an introduction to differential topology, the study of smooth manifolds through topological methods. A central theme is the analysis of mappings between manifolds and the properties preserved under diffeomorphisms. The course emphasizes how local phenomena can be connected to global structures, for example through Sard’s theorem and transversality. Fundamental results such as the Jordan–Brouwer separation theorem, the Borsuk–Ulam theorem, and classical connections between vector fields, fixed points, and curvature (including the Poincaré–Hopf, Lefschetz, and Gauss–Bonnet theorems) illustrate how differential topology unifies analysis, geometry, and topology.

Entry requirements

Mathematics MA, Topology, 7.5 credits, and Mathematics BA, 60 credits, including Mathematics BA, Multivariable Calculus, 7.5 credits.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Mathematics MA, Differential Topology

  Mid Sweden University

  Flexibel – Sundsvall

  Start date: 18 January 2027

  End date: 6 June 2027

  Pace of study: 25 %