- Docente: Massimo Ferri
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Learning outcomes
At the end of the course, the student is supposed to know the base
elements of algebraic topology, in particular of homotopy and of
homology groups. He/she shoud acquire the ability to compute
homology groups and fundamental group of the main examples of
(pseudo)manifolds.
Course contents
Categories and functors. Simplicial complexes and delta-complexes.
Homotopy. Fundamental group and edge group. Covering spaces.
Singular and simplicial homology. Exact sequences. Mayer-Vietoris
sequence. Orientation. CW-complexes. Higher homotopy groups.
Classification of surfaces. Eilenberg-Steenrod axioms.
Hints to: universal coefficients, cohomology, duality.
(Out of the exam program) Knots and links. Persistent homology and
size functions. Open problems in knot theory and in topology of
3-manifolds.
Readings/Bibliography
Lecture notes written by the lecturers.
Teaching methods
Class lectures.
Assessment methods
Homework and oral examination.
Teaching tools
Short seminars by young researchers.
Links to further information
http://www.dm.unibo.it/~ferri/
Office hours
See the website of Massimo Ferri