College:  Differentieerbare Varieteiten , najaar 2004.
               Differentiable Manifolds, fall 2004.

Docent: D. Siersma
 

Tweede deeltentamen en volledig tentamen 31 januari 2005

Aanvang cursus  : woensdag 8 september

collegetijd : woensdag   11 - 13   uur


Differentiable manifolds are generalizations of Euclidean spaces. Roughly speaking, any given point in a manifold has a neighborhood, which is
homeomorphic to an open set in Euclidean space. Familiar examples
are spheres, tori, projective spaces. One can develop part of
calculus on manifolds: integration, differentiation, vector fields, etc.
But manifolds also have other properties: global (related to the topology
of the manifold) and metric (related to curvature).

The concept of manifold is central in mathematics, but also many
physical theories (relativity theory, electromagnetism, gauge theory) have
a very geometric character and use differential manifolds in their descriptions.

 
The course on  the interface between bachelor and master studies.
It is good round off for the bachelor, but is also gives prerequisites
to many master courses, such as differential geometry, lie theory,
and courses in the theoretical physics master.
An options also to choose the course in the first semester
of the master programme. This is the reason to teach the course
in English.
 
Keywords are: Manifold, bundle, Lie derivative, differential form, Lie group.
Characteristic theorems are : De Rham and Stokes.

The course has many in common with Looijenga's course in the years before,
but there will also be some differences. If time allows we intend to make
an excursion to the beginnings of Morse theory.


The goal of the course is to get an good introduction into the subject.

As background for the course we use the lecture notes:
 Meetkunde op varieteiten (in Dutch) written by Prof. dr. E.J.N.Looijenga.
(available as .ps and .pdf file).
NB. The second part of the notes is meant for the Differential Geometry course
of Looijenga in period 3 and 4.

For relation with physics we advise to:
* Th. Frankel: The Geometry of Physics-an introduction. Cambridge University Press, 1997.
We intend to supply a list cross-references from  the Dutch notes to certain sections of Frankel.
   
 

Voor het college Differentieerbare variëteiten maken we gebruik van  het diktaat,:

Meetkunde op varieteiten, geschreven door Prof. dr. E.J.N.Looijenga,

dat hier beschikbaar is als postscript-bestand en als pdf-bestand.
(NB. De tweede helft van dit diktaat betreft het college Differentiaalmeetkunde.)

Referenties:

leerstof Eerste Deeltentamen maandag 8 november 2004

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