240023 Geometrie und Topologie (V) (SoSe 2023)
Contents, comment
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Diese Vorlesung gibt eine Einführung in die Topologie und ist die erste einer Reihe von Vorlesungen über Geometrie und Topologie. Die Topologie beschäftigt sich mit qualitativen Eigenschaften geometrischer Objekte. Der Begriffsapparat ist sehr allgemein und findet in fast allen Teilen der modernen Mathematik Anwendung.
Nach einer kurzen und systematischen Einführung topologischer Grundbegriffe und einer Diskussion universeller Konstruktionen werden insbesondere Kompaktheit und Zusammenhang besprochen. Der Begriff der Garbe wird im Kontext étaler Abbildungen diskutiert und bildet den Einstieg in die Überlagerungstheorie, dem topologischen Pendant der algebraischen Galois-Theorie. Die Rolle der algebraischen Galois-Gruppe übernimmt hierbei die topologische Fundamentalgruppe, welche mittels Zusammenhangskomponenten von Wegeräumen und Schleifenräumen konstruiert wird.
Inhalt:
1. Grundbegriffe der Topologie
2. Universelle Konstruktionen
3. Zusammenhang und Trennung
4. Kompaktheit
5. Garben
6. Überlagerungen
7. Fundamentalgruppen
Requirements for participation, required level
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Analysis 1&2, Lineare Algebra 1&2
Bibliography
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Laures, Szymik: Grundkurs Topologie
tom Dieck: Topologie
Teaching staff
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period |
|---|
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-B-GT-5 Geometry and Topology (5 CP) Geometrie und Topologie (5LP) | Geometrie und Topologie | Student information | |
| 24-B-GT_ver1 Geometry and Topology Geometrie und Topologie | Geometrie und Topologie | Graded examination
|
Student information |
| 24-M-GM Foundations in Mathematics Grundlagen Mathematik | Spezialisierungskurs Mathematik | Graded examination
|
Student information |
The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Studieren ab 50 |
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