MAGIC002: Differential topology and Morse theory

Course details

Semester

Autumn 2009
Monday, October 5th to Friday, December 11th

Hours

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

Timetable

Thursdays
09:05 - 09:55
Fridays
10:05 - 10:55

Description

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

Prerequisites

No prerequisites information is available yet.

Syllabus

  • 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.

Lecturer

  • DS

    Dr Dirk Schuetz

    University
    Durham University

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and 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

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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