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401-3006-00L 12 Credits

Differential Topology

Differentialtopologie

Lecturers & Examiners: Prof. Dr. Sebastian Baader
VVZ CR n/a

Last Updated: 2026-02-05 15:09:58

Abstract

Critical and regular points of differential mappings, Sard's theorem, Whitney's embedding theorem for compact manifolds; Morse theory and handle decompositions for differentiable manifolds, Reeb's theorem; degree of a mapping (via regular values and via differential n-forms), theorem of Poincare-Hopf about vector fields; Pontryagin's construction.

Content

Kritische und regulaere Punkte differenzierbarer Abbildungen, Satz von Sard, Einbettungssatz von Whitney fuer kompakte Mannigfaltigkeiten; Morsetheorie und Henkelzerlegungen fuer differenzierbare Mannigfaltigkeiten, Satz von Reeb; Grad einer Abbildung (via regulaere Werte und via n-Differentialformen), Satz von Poincare-Hopf ueber Vektorfelder; Konstruktion von Pontryagin.

Resources

Literature

M. W. Hirsch: Differential topology J. W. Milnor: Topology from the differentiable viewpoint J. W. Milnor: Morse theory S. Morita: Geometry of differential forms

General Information

Language
German
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Differentialtopologie
  • Mon 08:15-10:00 (HG G 5)
  • Fri 09:15-10:00 (HG G 3)
  • Fri 14:15-15:00 (HG G 26.5)
4 h weekly
exercise Differentialtopologie
  • Mon 15:15-16:00 (HG D 7.1)
  • Fri 08:15-09:00 (HG G 3)
2 h weekly

Offered In