Vrije Universiteit Amsterdam
Department of Mathematics


Home Publications CV Teaching Contact Links


Information for the student seminar "Topics in differential geometry: Morse theory" (Fall 2008):

The first meeting of the seminar will be on Friday, September 5, 13:30-16:15, room C648. At this meeting, an introductory lecture will be given and we will discuss all practical details.

Credits: 6

Period: 1+2 (Fall)

Aim: Introduce a specific topic in differential geometry or
differential topology by reading and presenting a book.
This year's topic is "Morse Theory".

Content: On a 2-sphere, the height function has two stationary points,
its maximum and minimum. On a tilted 2-torus it has four stationary
points though, two of which are of saddle-type. Morse theory studies
the relationship between functions defined on a manifold and the
topology of that manifold. One of the goals of this seminar is to
define the so-called Morse complex and to derive from it the Morse-
inequalities, which give a bound on the number of
stationary points of a function depending uniquely on the topology of
the manifold. Another goal is to introduce handle decompositions
associated to a Morse function and the theory of handlebodies, which
is a powerful method to visualize manifolds.
The theory contains a mix of topology and analysis and has
interesting consequences for topology, differential geometry and
dynamical systems.

Form of tuition: This is a student seminar. Students will be asked to
study the book on their own. The lecturers will give an introduction to
the subject and after this, students will be asked to present parts of the
book every week. After each presentation there will be time for
discussion.

Literature: Yukio Matsumoto, "An introduction to Morse Theory",
Translations of Mathematical Monographs (Volume 208), AMS 2002 (will
be provided)

Mode of assessment: The grade is determined by the quality, content and
clarity of the presentations. Active participation in the discussion will
also be taken into account.

Target audience: Master and PhD students in Mathematics

Coordinators: F. Pasquotto and B. Rink

Entry requirements: Differential geometry / differentiable manifolds.
Basic knowledge of topology and algebraic topology is helpful.