7.5 credits cr.
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Learn to state and prove basic theorems in algebraic topology, and compute the (co)homology of topological spaces and interpret the results geometrically.
The course covers:
- singular homology and cohomology of topological spaces
- exact sequences, chain complexes and homology
- homotopy invariance of singular homology
- the Mayer-Vietoris sequence and excision
- cell complexes and cellular homology
- the cohomology ring
- homology and cohomology of spheres and projective spaces
- applications such as the Brouwer Fixed Point theorem, the Borsuk-Ulam theorem and theorems about vectorfields on spheres
This course is given jointly by Stockholm University and KTH, and can be a part of the Master's Programme in Mathematics but may also be taken as a separate course.
The course consists of one element.
Instruction consists of lectures and exercises.
The course is assessed through written assignments and oral presentations of the assignments.
A list of examiners can be found on
ScheduleThe schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.
Note that the course literature can be changed up to two months before the start of the course.
A. Hatcher: Algebraic topology. Cambridge University Press.