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The course will describe basic material about smooth manifolds (vector fields, flows, tangent bundle, foliations etc), introduction to Morse theory, various applications.


Spring 2009 (Monday, January 19 to Friday, March 27)


  • Live lecture hours: 20
  • Recorded lecture hours: 0
  • Total advised study hours: 0


  • Thu 09:05 - 09:55
  • Fri 09:05 - 09:55


No prerequisites information is available yet.


  • Definition of differentiable manifolds and examples.
  • Tangent spaces and tangent bundles.
  • Regular values and Sard's Theorem.
  • Immersions, Submersions and transverse Intersections.
  • Whitney's Embedding Theorem.
  • Vector fields and flows.
  • Morse functions and Morse inequalities.
  • Brouwer degree.
  • Framed Cobordism and the Pontryagin construction.
The following books are recommended reading for the course:
  • G. Bredon, Topology and Geometry, Springer Verlag (Chapter 2).
  • J. Milnor, Topology from the Differentiable Viewpoint, Princeton University Press.
  • J. Milnor, Morse Theory, Princeton University Press.
  • L. Nicolaescu, An Invitation to Morse Theory, Springer Verlag.
  • F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer Verlag.


Dirk Schuetz
Phone (0191) 334 3089
Photo of Dirk Schuetz


Topology and GeometryBredon
Topology and GeometryBredon
Topology from the differentiable viewpointMilnor
Topology from the differentiable viewpointMilnor
Morse theoryMilnor
An Invitation to Morse TheoryNicolaescu
Foundations of differentiable manifolds and Lie groupsWarner


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No assessment information is available yet.

No assignments have been set for this course.

Recorded Lectures

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