- Docente: Roberto Pagaria
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Course contents
The aim of this course is to provide tools such as sheaves and spectral sequences useful for cohomology computations. This tools are used in various fields of mathematics: in complex geometry, differential geometry, commutative algebra, algebraic geometry and algebraic topology.
The course is divided into two parts: in the first we will briefly recall the definitions of homology and cohomology of a topological space and their main properties. We will see the main theorems (e.g. Kunneth, Lefschetz fixed point, Poincaré duality) and some of their applications to the computation of (co)homology groups.
In the second part we introduce the two important tools: sheaf theory and spectral sequences. Finally, we will apply these tools in algebraic topology by giving some examples.
Readings/Bibliography
Hatcher - Algebraic topology
Hatcher - Spectral sequences
Iversen - Cohomology of sheaves
Teaching methods
Theory lesson with examples and exercises.
Assessment methods
Oral exam. It will be evaluated whether to replace the oral with a seminar.
Office hours
See the website of Roberto Pagaria