2020/2021
Research Seminar "Topology I"
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Instructors:
Christopher Ira Brav
Language:
English
ECTS credits:
6
Contact hours:
60
Course Syllabus
Abstract
Topology studies a fairly general notion of space equipped with a notion of closeness. It is of importance in geometry and analysis. The course covers basic point-set topology, the classification of surfaces, and the theory of fundamental groups and covering spaces.
Learning Objectives
- The lectures cover basis material and examples, while the seminars allow students to more deeply explore the theory and examples.
Expected Learning Outcomes
- Students will become fluent in the basic notions of topology and will gain experience in the oral and written presentation of mathematics.
Course Contents
- Basic point-set topologyDefinition of topological space, open sets, closed sets, continuous functions
- Properties of topological spacesHausdorff, connected, compact
- Constructions of topological spacesQuotients, products, pushouts, pullbacks
- Fundamental groups and covering spacesDefinition of the fundamental group of a space. Relation between subgroups of the fundamental group and covering spaces. Calculations of fundamental groups using the van Kampen theorem.
- Classification of surfacesClassification of compact 2-dimensional manifolds with boundary.