- 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 Sep 17, 2024 to Dec 19, 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.
Applications: Classical Theorems of topology, invariance of domain, fixed point theorems. Jordan's separation theorem
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