Morse-Smale vector fields: definition, properties and induced structures

Abstract: In this talk we introduce some topics which are important for my second talk (which will be given in the TDA Seminar on the following day). We unpack the definition of Morse-Smale vector fields and discuss some of their properties, such as structural stability and genericity. We devote some time to the gradient-like case, which is closely linked to Morse theory. We see how in this case we can obtain a chain complex, called the Morse complex, as well as a CW decomposition of the underlying manifold. Time-permitting, we discuss the relation between Morse theory and persistent homology.

machine learning

Audience: general audience

Basic Notions and Applied Topology Seminar