DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCES
Master's Degree in Mathematics
Academic Year 2017/2018 - 1° Year

ELEMENTS OF ADVANCED GEOMETRY

Teaching Staff

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.

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