Differential Topology
Course, Master's level, 1MA259
Autumn 2023 Autumn 2023, 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
- 28 August 2023–14 January 2024
- 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
- 17 April 2023
- Application code
- UU-10061
Admitted or on the waiting list?
- Registration period
- 14 August 2023–10 September 2023
- Information on registration from the department
Autumn 2023 Autumn 2023, Uppsala, 33%, On-campus, English For exchange students
- Location
- Uppsala
- Pace of study
- 33%
- Teaching form
- On-campus
- Instructional time
- Daytime
- Study period
- 28 August 2023–14 January 2024
- 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
- 14 August 2023–10 September 2023
- Information on registration from the department
Autumn 2024 Autumn 2024, 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
- 2 September 2024–19 January 2025
- 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 2024
- Application code
- UU-10061
Admitted or on the waiting list?
- Registration period
- 19 August 2024–15 September 2024
- Information on registration from the department
Autumn 2024 Autumn 2024, Uppsala, 33%, On-campus, English For exchange students
- Location
- Uppsala
- Pace of study
- 33%
- Teaching form
- On-campus
- Instructional time
- Daytime
- Study period
- 2 September 2024–19 January 2025
- 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
- 19 August 2024–15 September 2024
- Information on registration from the department
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.
Contact
- Study counselling
- studievagledare@math.uu.se
- +46 18 471 32 03, +46 18 471 32 00