Topics in Differential Topology (U03421)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : MAT-4-DTop

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.

Entry Requirements

none

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Not being delivered

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Wednesday	14:00	14:50	KB

Summary of Intended 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.