Morse Thoery
Prerequisites
Basic knowledge of functional analysis, topolgy and geometry. Suggested for Master students, some parts
also for Ph.D. students depending on their background.
Programme
Reviev of algebraic topology
Morse's Lemma
Deformation lemma and habdle-body theorem
Morse inequalities
Manifolds with boundary and infinite-dimensional case
Applications, including ODEs, PDEs and theory of closed geodesics
Time permitting: Morse homology
Educational aims
The purpose of the course is to introduce Morse Theory, which links
the topolgy of a Riemannian variety to the structure of the critical points
critical points of a generic function defined on it. Several
then several applications. In particular, this theory shows
significant interaction between different branches of mathematics,
which are often treated in disjoint courses.
Bibliographical references
Milnor, Morse theory.
Nicolaescu, An invitation to Morse theory.
K.C. Chang, Infinite-dimensional Morse theory and multiple solution problems.
M. Schwarz, Morse homology.