- Singular and simplicial homology,
- computation of homology groups,
- cohomology,
- cup and cap product,
- Künneth formula,
- Poincaré duality.
Module MAT-40-16-M-6
Algebraic Topology (M, 9.0 LP)
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 |
---|---|
Position of the semester | 1 Sem. irreg. |
Level | [6] Master (General) |
Language | [EN] English |
Module Manager | |
Lecturers | |
Area of study | [MAT-AGCA] Algebra, Geometry and Computer Algebra |
Reference course of study | [MAT-88.105-SG] M.Sc. Mathematics |
Livecycle-State | [NORM] Active |
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")
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
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)
Requirements for attendance (informal)
Modules:
Courses
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-26-K-3] Introduction to Topology (2V+1U, 4.5 LP)
Requirements for attendance (formal)
None
References to Module / Module Number [MAT-40-16-M-6]
Course of Study | Section | Choice/Obligation |
---|---|---|
[MAT-88.105-SG] M.Sc. Mathematics | Pure Mathematics | [WP] Compulsory Elective |
[MAT-88.706-SG] M.Sc. Mathematics International | Pure Mathematics | [WP] Compulsory Elective |
Module-Pool | Name | |
[MAT-GM-MPOOL-5] | General Mathematics (Introductory Modules M.Sc.) |
Notice