Examination procedure
Oral exam (and paper to read for Ph.D. students)
Examination procedure notes
oral exam
Prerequisites
Basic knowledge of functional analysis, topology and
geometry. Suitable also for Master students.
Syllabus
Brief review of algebraic topology
Morse's Lemma
Deformation lemma and handle-body theorem
Morse inequalities
Manifolds with boundary and infinite-dimensional case
Lefschetz Teorem
ODEs with singular potentials
Morse-Smale theory
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.