Announcements


There are no announcements

Forum

General


Description

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.

Semester

Autumn 2017 (Monday, October 9 to Friday, December 15)

Timetable

  • Wed 13:05 - 13:55

Prerequisites

Basic knowledge of Differentiable Manifolds and Algebraic Topology is necessary. This can be obtained through the Core Courses MAGIC063 and MAGIC064.

Syllabus

  • 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.

Lecturer


Dirk Schuetz
Email dirk.schuetz@durham.ac.uk
Phone (0191) 334 3089
Photo of Dirk Schuetz


Students


Photo of Roberto Sisca
Roberto Sisca
(Surrey)


Bibliography


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


Note:

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.)

Assessment



No assessment information is available yet.

No assignments have been set for this course.

Files



No files have yet been uploaded for this course.

Recorded Lectures


Please log in to view lecture recordings.