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General


Description

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

Semester

Spring 2009 (Monday, January 19 to Friday, March 27)

Timetable

  • Thu 09:05 - 09:55
  • Fri 09:05 - 09:55

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


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


Students


Photo of Qusay S. A. Al-Zamil
Qusay S. A. Al-Zamil
(Manchester)
Photo of Azeb ALGHANEMI
Azeb ALGHANEMI
(Leeds)
Photo of Christopher Braun
Christopher Braun
(Leicester)
Photo of Philip Eve
Philip Eve
(Sheffield)
Photo of Damien Hartigan
Damien Hartigan
(Durham)
Photo of Anton Izosimov
Anton Izosimov
(Loughborough)
Photo of M. S. Jbara
M. S. Jbara
(Leeds)
Photo of Robert McKemey
Robert McKemey
(Manchester)
Photo of Beverley ONeill
Beverley ONeill
(Manchester)
Photo of Graham Reeve
Graham Reeve
(Liverpool)
Photo of Daniel Robinson
Daniel Robinson
(Manchester)
Photo of Miguel Rodriguez Olmos
Miguel Rodriguez Olmos
(Manchester)
Photo of Conor Smyth
Conor Smyth
(Liverpool)
Photo of Katie Steckles
Katie Steckles
(Manchester)
Photo of Pumei Zhang
Pumei Zhang
(Loughborough)


Bibliography


Topology and GeometryBredon
Topology and GeometryBredon
Topology from the differentiable viewpointMilnor
Topology from the differentiable viewpointMilnor
Morse theoryMilnor
An Invitation to Morse TheoryNicolaescu
Foundations of differentiable manifolds and Lie groupsWarner


Note:

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Assessment



No assessment information is available yet.

No assignments have been set for this course.

Recorded Lectures


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