MAU34201 Algebraic topology I
| Module Code | MAU34201 |
|---|---|
| Module Title | Algebraic topology I |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. David Wilkins |
| Module Prerequisites |
MAU22101 Group theory and one of
MAU22200 Advanced analysis MAU23203 Analysis in several real variables |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Students are assessed based on the exam alone.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Describe the definitions and basic properties of products and quotients of topological spaces.
- Describe in detail the construction of the fundamental group of a topological space, and justify with reasoned logical argument the manner in which topological properties of that topological space are reflected in the structure of its fundamental group.
- Justify with reasoned logical argument basic relationships between the fundamental group of a topological space and the covering maps for which that topological space is the base space.
Module Content
- Review of basic point set topology (topological spaces, continuous functions, Hausdorff spaces, connected spaces).
- Compact topological spaces.
- Product and quotient spaces.
- Covering maps and the Monodromy Theorem.
- The fundamental group of a topological space.
- Free discontinuous group actions.