MAU34201 Algebraic topology I
| Module Code | MAU34201 |
|---|---|
| Module Title | Algebraic topology I |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | |
| 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.
- Continuous assessment contributes 10% to the overall mark.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.
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 basic properties of topological spaces.
- Understand the construction of the fundamental group.
- Investigate covering spaces of topological spaces.
- Understand relations between the fundamental group and the underlying topological space
Module Content
- Review of basic topology
- Basics of the fundamental group.
- Coverings and liftings.
- Deck transformations and universal covering spaces.
- The Seifert–Van Kampen theorem.
- Classification of compact surfaces.