Provide tools and methods of algebraic topology, coomological theories and methods of homologous algebra.
teacher profile teaching materials
According to time and to interests of the class, we will also cover some of the following topics.
CW-complexes, Morse functions, persistent homology of manifolds associated to a Morse function, spectral sequences associated to persistent homology. Leray-Serre spectral sequences. Application to topological data analysis.
Cohomology, Poincaré duality, differential forms, De Rahm cohomology.
A. Hatcher: Algebraic Topology
Edelsbrunner, Harer, Computational Topology
Fruizione: 20410465 GE450 - TOPOLOGIA ALGEBRICA in Scienze Computazionali LM-40 CODOGNI GIULIO
Programme
Omology of topological spaces. Homotopy invariance, Mayer-Vietoris, excision, Kunneth formula. Examples and application. Vietoris-Rips and Chech complexes associated to a data set, persistent homology, application to topologicla data analysis.According to time and to interests of the class, we will also cover some of the following topics.
CW-complexes, Morse functions, persistent homology of manifolds associated to a Morse function, spectral sequences associated to persistent homology. Leray-Serre spectral sequences. Application to topological data analysis.
Cohomology, Poincaré duality, differential forms, De Rahm cohomology.
Core Documentation
A. Hatcher: Algebraic Topology
Edelsbrunner, Harer, Computational Topology
Type of delivery of the course
LecturesType of evaluation
Homeworks and final presentation.