Differential Topology

Utbildningsfakta

Kod: 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.

Behörighet

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.

Utbildningstillfällen

Varje tillfälle har egna datum och villkor. Avslutade tillfällen behålls som historik och innebär inte att en ny ansökan är öppen.

• Differential Topology

  Uppsala University

  Uppsala

  Startdatum: 31 augusti 2026

  Slutdatum: 17 januari 2027

  Studietakt: 33 %