Algebraic Topology (first part)
A.Y. 2025/2026
Learning objectives
(first part) The aim of the course is to introduce the main results and to provide some of the techniques of algebraic topology and of differential topology.
Expected learning outcomes
(first part) Know how to use some of the algebraic topology techniques on topological spaces and in particular on topological manifolds, and how to use some of the differential topology techniques on smooth manifolds.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
- Introduction to homological algebra. Introduction to some functors in algebraicc topology. In particular: singular homology groups, cellular homology for CW complexes, singular cohomology ring, universal coeffients theorem.
- Homotopy theory.
- Applications.
- Various tools to compute homology, cohomology and homotopy.
- Homotopy theory.
- Applications.
- Various tools to compute homology, cohomology and homotopy.
Prerequisites for admission
No specific prerequisites.
Teaching methods
Frontal lectures.
Teaching Resources
A. Hatcher, Algebraic topology, Cambridge University Press
J.P. May, A Concise Course in Algebraic Topology, Univ. Chicago Press
T. tom Dieck, Algebraic topology, EMS Press
J.P. May, A Concise Course in Algebraic Topology, Univ. Chicago Press
T. tom Dieck, Algebraic topology, EMS Press
Assessment methods and Criteria
The exam consists of an oral exam during which the student will be asked to illustrate some contents of the program of the course in order to evaluate her/his understanding of the contents of the course and her/his ability in applying them by solving some exercises.
Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
MAT/03 - GEOMETRY - University credits: 6
Practicals: 12 hours
Lessons: 35 hours
Lessons: 35 hours
Professor:
Stellari Paolo
Professor(s)
Reception:
Fix an appointment by email
Dipartimento di Matematica "F. Enriques" - Room 2046