MAGIC002: Differential topology and Morse theory

Course details

A specialist MAGIC course


Spring 2021
Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th


Live lecture hours
Recorded lecture hours
Total advised study hours


09:05 - 09:55 (UK)


The course will give an introduction to Morse Theory.

This theory studies the topology of smooth manifolds through real-valued smooth functions whose critical points satisfy a certain non-degeneracy condition.

We will investigate how the homotopy type is related to critical points and how the homology of a manifold can be calculated through Morse functions. 


Basic knowledge of Differentiable Manifolds and Algebraic Topology is necessary.

This can be obtained through the Core Courses MAGIC063 and MAGIC064. 


  • Smooth functions, non-degenerate critical points, Morse functions. 
  • Morse Lemma. 
  • Morse functions on spheres, projective spaces, orthogonal groups, configuration spaces of linkages. 
  • Homotopy type, cell decompositions of manifolds. 
  • Existence of Morse functions, cobordisms. 
  • Gradient flows, stable and unstable manifolds. 
  • Resonant Morse functions, ordered Morse functions. 
  • Morse homology, Morse inequalities. 
  • Calculations for projective spaces. 
  • Introduction to the h-cobordism theorem. 


  • DS

    Dr Dirk Schuetz

    Durham University


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The assessment for this course will be released on Monday 10th May 2021 at 00:00 and is due in before Monday 24th May 2021 at 11:00.

Assessment is via take-home examination. 

Please note that you are not registered for assessment on this course.


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