- 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 20, 2024 to May 31, 2024
Course contents
Cell complexes. Homotopy of maps and spaces.
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 coefficients 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, Rotman An introduction to 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