Geometry II
Academic Year 2025/2026 - Teacher: SANTI DOMENICO SPADAROExpected Learning Outcomes
After introducing the important category of topological manifolds, the main purpose of the course is to give the most basic elements of algebraic topology, focusing, in particular on homotopy and the fundamental group.
Required Prerequisites
A good knowledge of general topology.
Attendance of Lessons
Attending is strongly advised.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | General Topology review. | Chapters 1-5. |
| 2 | Complements of general topology. | Chapter 7. |
| 3 | Homotopy. | Chapter 10. |
| 4 | The fundamental group. | Chapter 11. |
| 5 | Covering spaces. | Chapter 12. |
| 6 | The Brouwer fixed point Theorem and the Borsuk-Ulam Theorem. | Chapter 12. |