There are no announcements




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.


Autumn 2012 (Monday, October 8 to Friday, December 14)


  • Tue 11:05 - 11:55


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.


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


Photo of Nada Alhabib
Nada Alhabib
Photo of Reem Alomair
Reem Alomair
Photo of Steven Charlton
Steven Charlton
Photo of Frederico De Oliveira
Frederico De Oliveira
(East Anglia)
Photo of Chris Draper
Chris Draper
Photo of Michela Egidi
Michela Egidi
Photo of Jonathan Grant
Jonathan Grant
Photo of Serena Liu
Serena Liu
Photo of Callan McGill
Callan McGill
Photo of Daniel Rust
Daniel Rust
Photo of Yafet Sanchez Sanchez
Yafet Sanchez Sanchez
Photo of Thomas Sutton
Thomas Sutton
Photo of James Walton
James Walton


Lectures on the h-cobordism theoremMilnor
An Invitation to Morse TheoryNicolaescu
Morse theoryMilnor
Lectures on Morse homologyBanyaga and Hurtubise
Topology and GeometryBredon
Foundations of differentiable manifolds and Lie groupsWarner


Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)


The Assessment for this course will be via a take-home examination, to be taken during the official assessment period between 7th and 18th of January 2013. The examination will consists of five questions, and you will need to obtain 40% to pass the course.

Final Examination for Differential Topology and Morse Theory

Files:Exam paper
Deadline: Friday 18 January 2013 (1889.5 days ago)

There will be a take-home examination for this course. The file will be made available on 7 January 2013. The exam consists of five questions. All five questions carry the same mark. To pass you need to get 40% of the total score. You are allowed to use the materials provided through the course website. You need to upload the answers to the MAGIC website by 18 January.

Recorded Lectures

Please log in to view lecture recordings.