Differential Topology
Course, Master's level, 1MA259
Expand the information below to show details on how to apply and entry requirements.
Autumn 2025 Autumn 2025, Uppsala, 33%, On-campus, English Only available as part of a programme
- Location
- Uppsala
- Pace of study
- 33%
- Teaching form
- On-campus
- Instructional time
- Daytime
- Study period
- 1 September 2025–18 January 2026
- Language of instruction
- English
- 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.
- Application deadline
- 15 April 2025
- Application code
- UU-10061
Admitted or on the waiting list?
- Registration period
- 18 August 2025–14 September 2025
- Information on registration from the department
Autumn 2025 Autumn 2025, Uppsala, 33%, On-campus, English For exchange students
- Location
- Uppsala
- Pace of study
- 33%
- Teaching form
- On-campus
- Instructional time
- Daytime
- Study period
- 1 September 2025–18 January 2026
- Language of instruction
- English
- 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.
Admitted or on the waiting list?
- Registration period
- 18 August 2025–14 September 2025
- Information on registration from the department
Expand the information below to show details on how to apply and entry requirements.
Autumn 2026 Autumn 2026, Uppsala, 33%, On-campus, English Only available as part of a programme
- Location
- Uppsala
- Pace of study
- 33%
- Teaching form
- On-campus
- Instructional time
- Daytime
- Study period
- 31 August 2026–17 January 2027
- Language of instruction
- English
- 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.
- Application deadline
- 15 April 2026
- Application code
- UU-10061
Admitted or on the waiting list?
Autumn 2026 Autumn 2026, Uppsala, 33%, On-campus, English For exchange students
- Location
- Uppsala
- Pace of study
- 33%
- Teaching form
- On-campus
- Instructional time
- Daytime
- Study period
- 31 August 2026–17 January 2027
- Language of instruction
- English
- 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.
Admitted or on the waiting list?
About the course
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.