Morse Theory

Academic year 2025/2026
Lecturer Andrea Malchiodi

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.