## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-40-16-M-6

## Module Identification

Module Number Module Name CP (Effort)
MAT-40-16-M-6 Algebraic Topology 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [6] Master (General) [EN] English Gathmann, Andreas, Prof. Dr. (PROF | DEPT: MAT) Gathmann, Andreas, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Schulze, Mathias, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Notice

Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-40-16-K-6
Algebraic Topology
P 84 h 186 h
U-Schein
- PL1 9.0 irreg.
• About [MAT-40-16-K-6]: Title: "Algebraic Topology"; Presence-Time: 84 h; Self-Study: 186 h
• About [MAT-40-16-K-6]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 84140 ("Algebraic Topology")

## Contents

• Singular and simplicial homology,
• computation of homology groups,
• cohomology,
• cup and cap product,
• Künneth formula,
• Poincaré duality.

## Competencies / intended learning achievements

Upon successful completion of this module, the students have studied the basic terms, propositions and techniques of algebraic topology. They understand how topological spaces and their properties can be described and classified by algebraic techniques. Moreover, they know how to compute these structures (homology, cohomology) in concrete cases. They understand the proofs presented in the lecture and are able to comprehend and explain them.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.

## Literature

• M.A. Armstrong: Basic Topology,
• A. Hatcher: Algebraic Topology,
• W.S. Massey: A Basic Course in Algebraic Topology.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

None

## References to Module / Module Number [MAT-40-16-M-6]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Pure Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Pure Mathematics [WP] Compulsory Elective
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)