Examination procedure
<p>Oral exam (and paper to read for Ph.D. students)</p>
Examination procedure notes
<p>oral exam</p>
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.