MTH4113 - Low-dimensional topology - 2019

The study of low-dimensional topology is the study of spaces of dimensions 2, 3, and 4, including the study of surfaces and their symmetries, knots and links, and structures on 3 and 4-manifolds. It has applications to mathematical fields such as geometry and dynamics; it also has modern applications to fields such as microbiology, physics, and computing. The unit will cover core concepts in low-dimensional topology such as surfaces and the mapping class group, descriptions of 3-manifolds by Heegaard splittings and Dehn fillings, cobordism in 4-dimensions. Additional topics may include prime and torus decompositions of 3-manifolds, knot and link invariants, contact and symplectic structures on manifolds, foliations, 3-manifold geometries, and applications to mathematical physics.

On completion of this unit students will be able to:

1. Formulate complex mathematical arguments using ideas from low-dimensional topology.
2. Apply sophisticated tools of low-dimensional topology to tackle novel problems, for example, to distinguish or classify new spaces, etc.
3. Communicate mathematical concepts and arguments.
4. Apply critical thinking to judge the validity of mathematical reasoning.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures
• 1-hour tutorial and
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics