MAU34306 Manifold topology
| Module Code | MAU34306 |
|---|---|
| Module Title | Manifold topology |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Florian Naef |
| Module Prerequisites |
MAU34301Differential Geometry |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards 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.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Prove theorems about the topology of manifolds.
- Understand the connection to algebraic topology via cobordisms.
- Explain the proof of the h-cobordism theorem.
- Explain the ingredients to the calculation of the cobordism rings.
Module Content
- Handle decompositions
- h-cobordism theorem
- Thom construction
- Cobordism rings
Recommended Reading
- Differential Topology by C.T.C. Wall
- Lectures on the h-cobordism theorem by John Milnor
- Characteristic Classes by John Milnor and James Stasheff