Differential Topology 2006  (Wis M 411)

Lecturer: Dirk Siersma
Mathematisch Instituut, Wiskundegebouw Room 520

Schedule

Monday       11:.00-13:00    
Wednesday   09:00-11:00

Planning of the course:

Feb 6  : Lecture	Feb 8:     Lecture
Feb 13: Lecture	Feb 15 : No lecture
Feb 20: Lecture	Feb 22: No lecture
Feb 27: Lecture	March 1: Lecture
March 6: No lecture	March 8: No lecture
March 13: Lecture	March 15: Lecture
March 20: NO Lecture (change !!)	March 22:NO Lecture (change !!)
March 27: Lecture !!	March 29: lecture !!
April 3: Lecture	April  5 : Lecture
April 10: No Lecture !!	April 12: Lecture !!
April 17: No lecture (eastern)	April 19: No lecture
April 24: Lecture	April 26: Last Lecture

Examination

The examination is oral.
You should make an appointment early enough since
I will be away at several occasions.
Eg:  april 27-may 18
       june 14 -30
       july 8-16
Anyhow try to finish before july 22, 2006.

You can contact me via :
email :  siersma@math.uu.nl
telephon: 030 2531475 (institute)
                035 525 7423 (home)
You should not only carefully study the course in detail,
but also choose a subject of at least one of the lectures
and compare that with the treatment in the references !!

Course Description:

Differential topology deals with the topological properties of differential manifolds.
Topics we intend to treat in the course are:

1. Morse Theory : the theory of critical point of functions on a manifold.
 (including a discription of the homotopy type of the manifold in terms of the
critical points, Morse inequalities)

2. De Rham Cohomology Theory of differential forms and applications

3. Intersection of (submanifolds) and degree of a map.

4. Curvature and critical point theory
(including a proof of the Gauss Bonnet theorem)

5. Miscellaneous

Aims

Master students in Mathematics and other science studebts with interest in topology and geometrty.

Literature

There is no book which cover the course completely. We intend to use different
sources, we mention some of them below. Also we will look for internet sources.

For the first part of the lecture (Morse Theory) we inetnd to use page 1-42 of:
J. Milnor : Morse Theory, Annals of Math. Studies 51, Princeton University Press.

Other sources:
R.Bott , L.W. Tu : Differential Forms in Algebraic Topology
V. Guilemin, A. Pollack : Differential Topology
J. Milnor: Topology from the differentiable viewpoint
M.W. Hirsch: Differential Topology

Prerequisites

A knowledge of differentiable manifolds. This includes standard analysis courses
and some parts of the bachelor coursae on differentiable manifolds.

Remarks

The course is (almost) completely disjunct from the Differentiable Geometry course
of Looijenga in the spring of 2005.


http://www.math.uu.nl/people/siersma/diftop06.html