Alessandro Sisto: Catalogue data in Autumn Semester 2019
|Name||Dr. Alessandro Sisto|
|401-3001-61L||Algebraic Topology I||8 credits||4G||A. Sisto|
|Abstract||This is an introductory course in algebraic topology, which is the study of algebraic invariants of topological spaces. Topics covered include:|
singular homology, cell complexes and cellular homology, the Eilenberg-Steenrod axioms.
|Literature||1) A. Hatcher, "Algebraic topology",|
Cambridge University Press, Cambridge, 2002.
Book can be downloaded for free at:
2) G. Bredon, "Topology and geometry",
Graduate Texts in Mathematics, 139. Springer-Verlag, 1997.
3) E. Spanier, "Algebraic topology", Springer-Verlag
|Prerequisites / Notice||You should know the basics of point-set topology.|
Useful to have (though not absolutely necessary) basic knowledge of the fundamental group and covering spaces (at the level covered in the course "topology").
Some knowledge of differential geometry and differential topology is useful but not strictly necessary.
Some (elementary) group theory and algebra will also be needed.
|401-5530-00L||Geometry Seminar||0 credits||1K||M. Einsiedler, P. Feller, U. Lang, A. Sisto, University lecturers|
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.
Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
|6 credits||13R||A. Sisto|
|Abstract||Topological spaces, continuous maps, connectedness, compactness, metric spaces, quotient spaces, homotopy, fundamental group and covering spaces, van Kampen Theorem.|
|Literature||James Munkres: Topology|
|Prerequisites / Notice||The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.|