Morse Thoery

Period of duration of course
Course info
Number of course hours
Number of hours of lecturers of reference
Number of hours of supplementary teaching

Type of exam

Oral exam


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Basic knowledge of functional analysis, topolgy and geometry.  Suggested for Master students, some parts 

also for Ph.D. students depending on their background. 


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.