Differential Topology

Education facts

Code: 1MA259

The course contains Manifolds, submanifolds, smooth maps, tangent space, and tangent bundles. The constant rank theorem. Immersions and embeddings. Submersions. Transversality. Sard's theorem. Brouwer's fixed-point theorem. Intersection theory modulo 2. Jordan-Brouwer's separation theorem. Orientation. Oriented intersection theory. Lefschetz's fixed-point theorem. The degree of a map. Hopf's degree theorem. Vector fields on manifolds and Poincaré-Hopf's theorem. Morse functions. Classification of one- and two-dimensional manifolds.

Entry requirements

120 credits including 90 credits in mathematics. Participation in Real Analysis. Basic Topology is recommended. Proficiency in English equivalent to the Swedish upper secondary course English 6.

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.

• Differential Topology

  Uppsala University

  Uppsala

  Start date: 31 August 2026

  End date: 17 January 2027

  Pace of study: 33 %