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Algebraic Topology (Small Specialization Module)
(dt. Algebraische Topologie (Kleines Vertiefungsmodul))

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS) oder lecture (2 SWS), seminar (2 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises or presentation with written assignment.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Volkmar Welker

Contents

Specialized topological methods are presented which contribute to the investigation of topological spaces, whcih are motivated by questions in algebra, algebraic geometry or combinatorics. These can be, for example, methods of homotopy theory or the theory of manifolds.


Qualification Goals

The students

  • know specialized topological constructions (e.g. from homotopy theory) and their algebraic invariants,
  • can use algebraic invariants of topological spaces in other areas (e.g. algebra, combinatorics),
  • can profitably apply methods from other areas (e.g. algebra, combinatorics) to topological questions.

They deepen

  • the practice of mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
  • in the recitation classes, their oral communication skills through discussion and free speech in front of an audience.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Algebra. In addition, the competences are recommended which are taught in an introductory course on topology.


Recommended Reading

  • de Longueville, Mark, A Course in Topological Combinatorics, Springer, 2011.
  • P.G. Goerss, R. Jardine, Simplicial homotopy theory, Birkhäuser 2010.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2019/20. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.