- 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 knows the base elements of
algebraic topology, in partucilar of homology and of the
fundamental group. He/she acquires the ability of computing
homology groups and fundamental group.
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. Classification of
surfaces.
Hints at: universal coefficients, cohomology, duality; higher homotopy groups.
Readings/Bibliography
Lecture notes.
C.R.F. Maunder, "Algebraic Topology", Cambridge Univ. Press,
1980.
E.H. Spanier, "Algebraic Topology", McGraw-Hill 1966.
A. Hatcher, "Algebraic Topology", Cambridge Univ. Press, 2002. Freely
downloadable.
Teaching methods
Lecture of traditional type.
Assessment methods
Oral exam, preceded by the solution of the exercises downloadable
here:
http://www.dm.unibo.it/~ferri/hm/progtopalg.htm
Links to further information
http://www.dm.unibo.it/~ferri/
Office hours
See the website of Massimo Ferri