20410341 - GE220 - Topology

Acquire a good knowledge of concepts and methods of general topology, with particular regard to the study of the main properties of topological spaces such as connection and compactness. Introduce the student to the basic elements of algebraic topology, through the introduction of the fundamental group and the topological classification of curves and surfaces.

Curriculum

teacher profile | teaching materials

Programme

Introduction to point-set topology: products, connections, compactness and metric spaces.
Homotopy and the fundamental group.

Core Documentation

Course notes by prof. Caporaso
Munkres - Topology

Reference Bibliography

E. Sernesi: Geometria 2, Bollati Boringhieri, 2001. N. Bourbaki: General Topology, Volume 1, Springer, 1989. S. Willard: General Topology, Dover Publications, 2004. J. L. Kelley: General Topology, Graduate Text in Mathematics, Springer 1975. A. Hatcher: Algebraic Topology, Cambridge University Press, 2002.

Type of delivery of the course

In person lectures, exercise sessions.

Attendance

Either in person or online via Teams

Type of evaluation

2 midterms. Final written exam. Compulsory oral exam.

teacher profile | teaching materials
teacher profile | teaching materials

Programme

Introduction to point-set topology: products, connections, compactness and metric spaces.
Homotopy and the fundamental group.

Core Documentation

Course notes by prof. Caporaso
Munkres - Topology

Reference Bibliography

E. Sernesi: Geometria 2, Bollati Boringhieri, 2001. N. Bourbaki: General Topology, Volume 1, Springer, 1989. S. Willard: General Topology, Dover Publications, 2004. J. L. Kelley: General Topology, Graduate Text in Mathematics, Springer 1975. A. Hatcher: Algebraic Topology, Cambridge University Press, 2002.

Type of delivery of the course

In person lectures, exercise sessions.

Attendance

Either in person or online via Teams

Type of evaluation

2 midterms. Final written exam. Compulsory oral exam.

teacher profile | teaching materials