Complexes de type Morse et leurs équivalences
In this thesis, we study aspects of Morse theory and the chain complexes that derive from it : the Morse complex, the Milnor complex and the Barraud-Cornea complex. Using different techniques from differential topology and Morse theory, which will be presented in the first chapters, we carefully build these complexes before proving their equivalence. This thesis synthesises and compares three points of view in Morse theory in a document accessible to beginning graduate students.
CW-complexes Morse theory Morse complex Critical points CW-complexes Connecting manifold Blow-up of the unstable manifold