Algebraic Topology
10 credits
Syllabus, Master's level, 1MA197
A revised version of the syllabus is available.
- Code
- 1MA197
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 21 March 2013
- Responsible department
- Department of Mathematics
Entry requirements
120 credits including 90 credits in mathematics. Real Analysis or equivalent.
Learning outcomes
In order to pass the student should be able to
- define the various geometric and algebraic concepts introduced and apply and interpret them in concrete examples;
- formulate and apply central theorems in deRham theory and present their proofs;
- use the theory methods and techniques of the course for problem solving.
Content
The de Rham Complex on Rn. Orientation and Integration, Stoke's theorem. Poincare Lemmas. The degree of a proper map. The Mayer-Vietoris sequence. Poincare duality on an orientable manifold. The Kunneth formula and the Leray-Hirsch theorem. The Poincare dual of a closed oriented submanifold. The Thom Isomorphism. Vector bundles and cohomology. Poincare duality and the Thom class. The Euler class and the Thom class.
Instruction
Lectures and problem solving lessons.
Assessment
Written examination and compulsory assignments during the course.