Undergraduate Course: Topics in Differential Topology (MATH10039)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Course for final year students in Honours programmes in Mathematics.
1. Define smooth manifolds and give lots of interesting
examples, perhaps concentrating on surfaces in 3-space.
2. Define de Rham cohomology and perhaps compare it with
simplicial cohomology.
3. Study the topology of manifolds (surfaces) via Morse
functions. |
| Course description |
Not entered
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
1. Familiarity with simple examples of smooth manifolds.
2. Familiarity with differential forms, de Rham cohomology
and its relation with combinatorial definitions of
cohomology.
3. Familiarity with Morse functions and their use in the
calculation of topological invariants of a manifold.
4. Familiarity with further topics in differential
topology, such as the Hopf index theorem, Lefschetz
fixed-point theorem.
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Contacts
| Course organiser | Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: |
Course secretary | Ms Jennifer Marshall
Tel: (0131 6)50 5048
Email: |
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