241022 Differentialformen in der algebraischen Topologie (Differential forms in algebraic topology) (S) (SoSe 2024)

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Differentialformen bilden eine Schnittstelle zwischen Differentialgeometrie und algebraischer Topologie. Die Definitionen des de Rham Komplexes und der de Rham Kohomologie sind eventuell schon aus anderen Veranstaltungen bekannt. Das hier angebotene Seminar orientiert sich an dem gleichnamigen Buch "Differential Forms in Algebraic Topology" von Raoul Bott und Loring Tu, in dem tieferliegende Aspekte der de Rham Kohomologie behandelt werden. Dabei werden viele Konzepte der algebraischen Topologie mit Hilfe von Differentialformen veranschaulicht. Ziel ist es, das Buch so weit wie möglich durchzuarbeiten.

Requirements for participation, required level

Vorkenntnisse über Differentialformen und homologische Algebra (Kettenkomplexe, Homologie, etc) sind hilfreich aber nicht zwingend notwendig. Im Prinzip sind Grundkenntnisse über differenzierbare Mannigfaltigkeiten und ein Interesse an algebraischer Topologie ausreichend.

Bibliography

Bott, Tu - Differential Forms in Algebraic Topology (Springer, Graduate texts in mathematics, volume 82)

Teaching staff

Dates ( Calendar view )

Frequency Weekday Time Format / Place Period  
weekly Fr 12-14 V5-148 08.04.-19.07.2024

Subject assignments

Module Course Requirements  
24-M-P1 Profilierung 1 Profilierungsseminar Study requirement
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24-M-P1a Profilierung 1 Teil A Profilierungsseminar Study requirement
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24-M-P1b Profilierung 1 Teil B Profilierungsseminar Study requirement
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24-M-P2 Profilierung 2 Profilierungsseminar Study requirement
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24-M-PWM Profilierung Wirtschaftsmathematik Profilierungsseminar Study requirement
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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    

Je nach Teilnehmerzahl wird das Konzept zwischen einem klassischen Seminar mit wöchentlichen Vorträgen und einer Art Lesekurs mit regelmäßigen Diskussionen und gelegentlichen Vorträgen variieren. Grundsätzlich wird allerdings die Bereitschaft erwartet, sich jede Woche mit der Literatur (ca. 10 Buchseiten) zu beschäftigen.

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Last update basic details/teaching staff:
Wednesday, January 3, 2024 
Last update times:
Thursday, April 11, 2024 
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Thursday, April 11, 2024 
Type(s) / SWS (hours per week per semester)
S / 2
Department
Faculty of Mathematics
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