Key facts
Details for course being taught in current academic year
Level 3 - 15 credits - spring term
Resources
Course description
Course outline
Algebraic Topology is a discipline where various concepts from Algebra in particular Group theory are borrowed to study and characterise topological spaces. It is a very rewarding subject to study in the undergraduate and graduate level and is an active research area with still many interesting open problems. This course introduces the students to the concepts of homology and cohomology groups, provide them with the necessary computational skills to evaluate these groups for various spaces such as 2-manifolds, n-spheres and projective spaces. Some applications including the Brouwer fixed point theorem, Jordan separation theorem and Schonflies theorem will be discussed. Moreover, the notion of homotopy groups will be introduced and various examples will be given.
Pre-requisite
Linear Algebra, Groups and Rings
Learning outcomes
1 State and understand the classification theorem for compact 2-manifolds.
2 Understand the concepts of homology and cohomology groups associated with topological spaces and be able to compute these groups for a number of important spaces.
3 Understand the concept of homotopy groups associated with pointed topological spaces and be able to compute these groups for a number of important spaces.
4 Understand the concepts of exact sequences associated with homology groups, homotopy groups and fibrations.
Library
1) Introduction to Algebraic Topology, J.J. Rotman
2) Homotopy Theory, S.T. Hu,
3) Homology Theory, W. Vicks
4) Topology and Geometry, G. Bredon
Assessments
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 25.00% | |
| Problem Sets | Spring Week 3 | 25.00% |
| Problem Sets | Spring Week 5 | 25.00% |
| Problem Sets | Spring Week 7 | 25.00% |
| Problem Sets | Spring Week 9 | 25.00% |
| Unseen Examination | Summer Term (2 hours) | 75.00% |
Resit mode of assessment
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Summer Vacation (2 hours ) | 100.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
Teaching methods
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring Term | LECTURE | 2 hours | 1111111111 |
| Spring Term | WORKSHOP | 1 hour | 0101010101 |
| Spring Term | LECTURE | 1 hour | 1010101010 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.