MATS4100 Introduction to Geometric Group Theory (3 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
Content
•Fundamental group, covering map, universal cover.
•Group action by isometries, finitely generated group, Cayley graph.
•Geometric action, Svarc-Milnor Lemma.
•The growth of a group, volume growth of a manifold, Gromov's theorem on polynomial growth.
•Hyperbolic space and manifold, Gromov hyperbolic metric spaces and groups.
•Amenable groups and the Banach Tarski paradox.
Completion methods
To pass the course, each student is required to present a problem on the board during the exercise sessions and to take the written exam
Learning outcomes
•Become familiar with some of the objects/groups studied in Geometric Group Theory: finitely generated groups, Cayley graphs, isometric action on metric spaces.
•Understand geometric actions and their genericity (Svarc-Milnor Lemma)
•Understand some connections between Group Theory and Geometry, e.g. the importance of the fundamental group of a manifold, etc.
•Learn some of the comparison tools of Coarse Geometry: Lipschitz map, bi-Lipschitz equivalence, quasi-isometric map, quasi-isometry, etc.
•Become familiar with some of the most important theorems of GGT.
•Understand geometric actions and their genericity (Svarc-Milnor Lemma)
•Understand some connections between Group Theory and Geometry, e.g. the importance of the fundamental group of a manifold, etc.
•Learn some of the comparison tools of Coarse Geometry: Lipschitz map, bi-Lipschitz equivalence, quasi-isometric map, quasi-isometry, etc.
•Become familiar with some of the most important theorems of GGT.
Description of prerequisites
Metric spaces, Algebra 1: Rings and Fields and Algebra 1: Groups
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
x
Teaching (3 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English