SF2735 Homological Algebra and Algebraic Topology 7.5 credits

1. Homological algebra:  homomorphisms, kernels cokernels,  exact sequences and complexes, Snake lemma, functorial properties of Hom(A,B) and the tensor product,  Tor and Ext groups, Universal Coefficient Theorem.
2. Topology: euclidian and projective spaces, singular homology  and its properties, fundamental group, applications: Brouwer fix point theorem and non-vanishing vector fields on spheres.

The aim of the course is to discuss basics of homological algebra and topology and illustrate how one can use one to  understand the other. The focus will be on the construction of homology for both chain complexes and topological spaces. The aim is to develop methods used for calculations and learn how to interpret the answer.

120 university credits (hp) including the course "Groups and rings" (SF2729) or corresponding course, and documented proficiency in English corresponding to English B.

• TEN1 - Examination, 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.

If the course is discontinued, students may request to be examined during the following two academic years.

Written examn/home assignments (where slash means and/or, all depending on what we decide to do at a much later stage.)

Mats Boij

• 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.