Research Seminar "Topology I"
- The lectures cover basis material and examples, while the seminars allow students to more deeply explore the theory and examples.
- Students will become fluent in the basic notions of topology and will gain experience in the oral and written presentation of mathematics.
- 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.
- Interim assessment (2 module)0.4 * Final Exam + 0.4 * Midterm exam + 0.2 * Seminar participation