The left-orderable vonNeumann-Day problem

Disciplines

Mathematics (100%)

Keywords

Geometric Group Theory, Small Cancellation Theory, Left-Orderable Groups, Simple Groups, Tarski monsters, Unique Product Property

Abstract

In this project, we are interested in dynamical, algebraic and geometric properties of groups. A group is an abstract mathematical object that encodes the symmetries of an underlying space. For example, the rotations and translations in the Euclidean plane generate a group. We will in particular work on so-called left-ordered groups. These groups consist of symmetries of the real line that preserve the natural order "larger", "equal", "smaller" on the real line. We plan to study and find such groups with particularly surprising properties. Like this we want to contribute to important open question on left-ordered groups.