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Algebraic Topology II (Large Specialization Module)
(dt. Algebraische Topologie II (großes Vertiefungsmodul))

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 (individual examination)
Language,
Grading		 English,
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. Oliver Goertsches, Prof. Dr. Sönke Rollenske

Contents

Possible topics include:

  • ordinary cohomology theories and Poincaré duality.
  • homotopy groups
  • Fibers and cofibrations
  • Eilenberg-MacLane spaces
  • spectral sequences
  • Equivariant cohomology
  • Characteristic classes

Qualification Goals

The students

  • know common and also advanced topological constructions,
  • master the interplay between algebra and topology,
  • understand connections between different subfields of algebraic topology (e.g., homology, cohomology, homotopy) and also adjacent fields,
  • can recognize and use functorial relations.
  • have deepened mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in exercises 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, Algebraic Topology I.


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.


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
  • Stöcker, Ralph und Zieschang, Heiner: Algebraische Topologie. Springer, 1994
  • Tu, Loring W.: Introductory Lectures on equivariant cohomology, Princeton University Press, 2020



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

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.