MTH4113 Low-dimensional topology
Faculty of Science
MTH4113 Low-dimensional topology is a level 4, 6-credit-point, postgraduate unit from the Faculty of Science. It isn't offered in 2025. It has no prerequisites.
- Credit points
- 6
- Offered in 2025
- Not offered
- Assessment
- Exam 50%
- and 1 other task
This is the 2025 handbook entry. See the 2027 entry.
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Requisites
Before MTH4113
No prerequisites or corequisites besides the enrolment rules below.
After MTH4113
No unit lists MTH4113 as a prerequisite in the 2025 handbook.
Enrolment rules
PROHIBITION: MTH5113
COREQUISITE: Enrolment in the Master of Mathematics.
PREREQUISITE: MTH3130
Equivalent units
The same content under another code. Only one of them counts.
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.
Offerings in 2025
The 2025 handbook lists no offerings for MTH4113.
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Learning outcomes
When you finish this unit, you should 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.
- 3
Communicate mathematical concepts and arguments.
- 4
Apply critical thinking to judge the validity of mathematical reasoning.
Workload and teaching
- Applied sessions11 hours
- Seminars36 hours
- Teaching approachActive learning
- Two 1.5 -hour seminars;
- One 1-hour applied class (in weeks 2-12) and
- 8 hours of independent study per week.
Active learning will occur in lectures and applied classes.
Contacts
- Chief Examiners
- Professor Jessica Purcell
- Unit Coordinators
- Professor Jessica Purcell
Common questions
What are the prerequisites for MTH4113?
MTH4113 has no prerequisites, but enrolment rules apply.
When is MTH4113 offered?
MTH4113 has no offerings listed in the 2025 handbook.
Does MTH4113 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.