Number of credits: 8 hp
Examiner: Vitalij Tjatyrko
Course literature: J.R. Munkres:
1. Topology, Prentice Hall, 2000, and
2. Elements of algebraic topology, Addison Wesley Publishing Company 1993.
Course contents: Quotient maps, quotient spaces. Homotopy, fundamental group.
Covering spaces. The fundamental group of circle. Free abelian groups, direct sums, finitely generated abelian groups. Simplicial complexes, homology groups of a simplicial complex, relative homology. The computability of homology groups. Topological invariance of the homology groups. The exact homology sequence, Mayer-Vietoris sequence. The Eilenberg- Steenrod axioms. Applications of the homology theory to classical problems of geometry and topology.
Organisation: Eleven lectures, eleven lists of assignments and four problem seminars.
Examination: Active participation in the problem seminars.
Prerequisites: General topology (basics) and abstract algebra (basics)
Last updated: 2019-05-20