This entry is from Winter semester 2018/19 and might be obsolete. You can find a current equivalent here.

# Elementary Topology (dt. Elementare Topologie)

 Level, degree of commitment Advanced module, depends on importing study program Forms of teaching and learning,workload Lecture (3 SWS), recitation class (1 SWS), 180 hours (60 h attendance, 120 h private study) Credit points,formal requirements 6 CP Course requirement(s): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Subject, Origin Mathematics, B.Sc. Mathematics Duration,frequency One semester, irregular Person in charge of the module's outline Prof. Dr. Ilka Agricola

## Contents

• Topological spaces and manifolds
• Elementary properties of topological spaces: compactness, orientability, boundary. Many examples: Möbius band, Klein's bottle, projective space etc.
• Classification of surfaces, genus of a surface, triangulations, Boy's surface
• Euler Characteristic and Euler's polyhedron theorem
• Fundamental group, mapping degree and coverings

## Qualification Goals

The students shall

• understand basic principles of topological structures and recognize that such structures can be found in many parts of mathematics,
• practice axiomatic procedures and train their abstraction skills,
• practice mathematical working methods (development of mathematical intuition and its formal justification, proof techniques),
• improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

## Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden.

• Boltjanskij, V.G. und Efremovic, V.A.: Anschauliche kombinatorische Topologie. VEB Deutscher Verlag der Wissenschaften (1986).
• Hatcher, A.: Algebraic topology. Cambridge University Press (2002).
• Hu, S.-T.: Homotopy Theory. Academic Press (1959).
• Ossa, E.: Topologie. Vieweg-Verlag (1992).
• Pontrjagin, L.S.: Grundzüge der kombinatorischen Topologie. VEB Deutscher Verlag der Wissenschaften (1956).
• Stöcker, R. und Zieschang, H.: Algebraische Topologie. Eine Einführung. Teubner-Verlag (1988).