Morse Theory

Academic year 2025/2026
Lecturer Andrea Malchiodi

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.