Hide menu

Polopoly will be shut down December 15, 2023. Existing pages will have to be moved or removed before that date. Empolyees may read more at FAQ Polopoly Avveckling

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)

Page manager: karin.johansson@liu.se
Last updated: 2019-05-20