This entry is from Winter semester 2016/17 and might be obsolete. You can find a current equivalent here.

# Elementary Topology (dt. Elementare Topologie)

 Level, degree of commitment Advanced module, compulsory elective module 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. 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

Students should

• understand basic principles of topological structures and recognize that such structures are found in many parts of mathematics,
• practice axiomatic procedures and train their ability to abstract,
• practice mathematical working methods (develop mathematical intuition and its formal justification, train their ability to abstract, reason),
• improve their oral communication skills in the exercises by practicing free speech in front of an audience and in discussion.

## Prerequisites

Translation is missing. Here is the German original:

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

## Applicability

Module imported from B.Sc. Mathematics.

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

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

When studying M.Sc. Computer Science, this module can be attended in the study area Minor subject Mathematics.

• 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).