Differential Topology 2006 (Wis M 411)
Lecturer: Dirk Siersma
Mathematisch Instituut, Wiskundegebouw Room 520
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 |
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
Master students in Mathematics and other science studebts with interest in topology and geometrty.
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
A knowledge
of differentiable manifolds.
This includes standard analysis courses
and some parts
of the
bachelor coursae on
differentiable manifolds.
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