6FMAI06
Algebraic topology

(replaces MAI0040)

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)

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Last updated: 2019-05-20