Morse Theory
Prerequisiti
Basic knowledge of functional analysis, topology and
geometry. Suitable also for Master students.
Programma
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
Obiettivi formativi
The purpose of the course is to analyze the relationships between the topology of varieties and the structure of critical points
of regular functions defined on them. In-depth study of these topics should help students to develop connections between analysis, geometry and topology.
Riferimenti bibliografici
Milnor, Morse theory.
Nicolaescu, An invitation to Morse theory.
K.C. Chang, Infinite-dimensional Morse theory and
multiple solution problems.
M. Schwarz, Morse homology.