MTH5113 · Low-dimensional topology

Overview

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.

Areas of study: Master of Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

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;
3. Communicate mathematical concepts and arguments;
4. Apply critical thinking to judge the validity of mathematical reasoning.

Workload

• Two 1.5 -hour seminars; • One 1-hour applied class (in weeks 2-12) and • Eight hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.