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This entry is from Winter semester 2022/23 and might be obsolete. No current equivalent could be found.

Algebraic Topology
(dt. Algebraische Topologie)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker

Contents

Algebraic invariants of topological spaces are constructed (homology, cohomology or homotopy). As application elegant solutions for classical problems of topology are derived (invariance of dimension, fixed point theorems).


Qualification Goals

The students

  • know basic topological constructions,
  • can use algebraic invariants to solve topological problems,
  • can recognize and use functorial relationships.

They deepen

  • the practice of mathematical methods (development of mathematical intuition and its formal justification, training of the ability of abstraction, formulations of proofs),
  • 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, we recommend the knowledge of topology that will be taught in an introductory course.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

The module can also be used in other study programs (export module).

The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.


Recommended Reading

  • Hatcher, Allen Algebraic topology. Cambridge University Press, Cambridge, 2002.
  • May, J. P. A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2022/23. 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.