MAGIC002: Differential topology and Morse theory

Course details

Semester

Spring 2008
Monday, January 21st to Friday, March 14th; Monday, April 28th to Friday, May 16th

Hours

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

Timetable

Mondays
13:05 - 13:55
Fridays
13:05 - 13:55

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

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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