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Content and learning outcomes
- Singular homology and cohomology of topological spaces
- Exact sequences, chain complexes, and homology
- homotopy invariance of singular homology
- 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 hairy ball theorem, Brouwer’s fixed point theorem and the Borsuk-Ulam theorem
Intended learning outcomes
After completing the course, the student will be able to:
- formulate and prove basic theorem in algebraic topology
- compute the (co)homology of topological spaces and interpret the results geometrically.
Literature and preparations
Completed courses SF1678 Groups and Rings.
Announced no later than 4 weeks before the start of the course on the course web page.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- ÖVN1 - Assignment, 7.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The examiner decides about adapted examination for students with documented, severe disabilities in consultation with the contact person for disabilities at KTH (Funka). The examiner may allow a different form of examination for re-examination of individual students.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web SF2750