- Docente: Luca Migliorini
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
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from Feb 24, 2023 to May 26, 2023
Course contents
Cell complexes. Homotopy of maps and spaces.
The fundamental group. Homotopy invariance and dependance upon the base point.
Free and amalgamated products of groups. The Seifert Van Kampen theorem. Application to graphs.
Covering of a topological space. Lifting proeprties, Covering and fundamental group.
Singular and simplicial homology of a topological space. Excision theorem, Mayer Vietoris exact sequence. Sketch of Hurewicz theorem.
Cohomology and its relation with homology. Cup product. Poincaré duality for topological manifolds. Axioms for cohomology.
Universal coefficints Theorems. Ext and Tor groups.
A sketch of sheaf cohomology.
Applications: Classical Theorems of topology, invariance of domain, fixed point theorems.
Readings/Bibliography
A. Hatcher: Algebraic Topology
Teaching methods
Lectures at the blackboard
Assessment methods
Oral exams and exercises given during the course.
Office hours
See the website of Luca Migliorini