TOPOLOGIA ALGEBRICA
Academic Year 2022/2023 - Teacher: Angelo BELLAExpected Learning Outcomes
Fundamental aspects of Algebraic Topology. Principal objects of the study are the omotopy theory and the singular homology groups.
Course Structure
Lectures with slides. Discussion and correction of exercises.
If the teaching is given in a mixed or remote mode, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus.
Detailed Course Content
Basic facts on algebraic topology. Homotopy theory. Degree of a function between n-spheres. Brower's theorem in general form. Singular homology groups. The exact sequence of a pair. Mayer-Vetoris's sequence. Another proof of Brower's theorem. Jordan's theory in general form.
Textbook Information
1. Professor's notes
2. "Topologia" by M. Manetti.
3. W. Massey"Singular homology theory
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Richiami sulla definizione e le proprietà di base del gruppo fondamentale. | |
| 2 | Omeomorfismi locali | |
| 3 | Rivestimenti | |
| 4 | Quozienti per azioni propriamente discontinue | |
| 5 | Monodronia | |
| 6 | Il teorema di Van Kampen. | |
| 7 | Introduzione alla omologia singolare. | |
| 8 | Gruppi di omologia e morfismi associati. | |
| 9 | Omologia relativa | |
| 10 | La sequenza esatta di omologia. | |
| 11 | La proprietà di escissione | |
| 12 | Esempi di calcolo di gruppi di omologia | |
| 13 | Applicazioni |