ELEMENTS OF ADVANCED GEOMETRY
Academic Year 2018/2019 - 1° Year - Curriculum DIDATTICO and Curriculum TEORICO- First part.: Angelo BELLA
- Second part.: Angelo BELLA
Scientific field: MAT/03 - Geometry
Taught classes: 70 hours
Exercise: 24 hours
Term / Semester: 1° and 2°
Learning Objectives
- First part.
For both parts. The student will learn methods of set theory taht will be applied to general topology. Then he will learn some basic facts of algebraic topology and differential geometry.
- Second part.
For both parts. The student will learn methods of set theory taht will be applied to general topology. Then he will learn some basic facts of algebraic topology and differential geometry.
Course Structure
- First part.
Lectures with slides. Discussion and correction of exercises.
- Second part.
Lectures with slides. Discussion and correction of exercises.
Detailed Course Content
- First part.
Introduction to set theory.Ordinals and cardinals. Filters and Ultrafilters. The space of all ultrafilters on the integers. Complements of general topology.
- Second part.
Omotopy of functions and paths. The construction of the fundamental group. Applications. Fixed point theorem in dimenion 2. The Jordan's curve theorem. Introduction to differential manifolds.
Textbook Information
- First part.
1. Notes of the lecturer.
2.Topologia di M. Manetti.
- Second part.
1. Notes of the lecturer.
2. Topologia di M. Manetti