MT5869 Geometric Group Theory

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Module runs in even years only (2024/25, 2026/27, 2028/29, etc)

Planned timetable

10am Monday (odd weeks), Wednesday, Friday at 10am

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr C P Bleak

Dr C P Bleak
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

Geometric group theory is an important and active area of mathematical research, linking the geometry of various spaces, and in particular of a group’s Cayley graph, to the algebraic structure of the group. This module develops foundational tools and concepts in this field, including the fundamental group, which associates a group to a topological space, the Švarc-Milnor Lemma, which allows one to consider finitely generated groups as geometric objects, and Gromov-hyperbolic groups, which are groups with particularly nice geometric realisations and useful algebraic presentations. The module will introduce students to these concepts and techniques, and enable them to analyse groups from this powerful geometric perspective through exploration and problem solving.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT4003 AND PASS MT4526

Assessment pattern

100% Written Examination

Re-assessment

100% Oral Examination

Learning and teaching methods and delivery

Weekly contact

2.5h lectures (x10 weeks) 1 tutorial (x9 weeks)

Scheduled learning hours

34

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

116

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Construct free groups and demonstrate an understanding of their basic properties.
  • Construct a group given by a presentation, and demonstrate an understanding of standard problems concerning finitely-presented groups, including the word, conjugacy and isomorphism problems.
  • Work with groups as geometric objects, including the representations as groups of automorphisms of their own Cayley graphs, and as the fundamental group of a topological space X.
  • Understand and use the Švarc-Milnor Lemma.
  • Prove key results about hyperbolic groups.