Syllabus
- basic topological notions: topological space, continuous map, homeomorphism
- simplicial complexes and complexes on data: Čech, Delaunay, Vietoris-Rips
- homotopy, homotopy equivalence, fundamental groups
- homology, homology groups, Betti numbers, relative homology
- persistent homology, filtrations, persistent algorithm, persistent diagram, stability
Annotation
The lecture introduces basic notions of computational topology.