Topologically speaking, left-orderable countable groups are precisely those countable groups that embed into the group of orientation preserving homeomorphisms of the real line. A recent advancement in the theory of left-orderable groups is the discovery of finitely generated left-orderable simple groups by Hyde and Lodha. We will discuss a construction that extends this result by showing that every countable left-orderable group is a subgroup of such a group. We will also discuss some of the algebraic, geometric, and computability properties that this construction bears. The construction is based on novel topological and geometric methods that also will be discussed. The flexibility of the embedding method allows us to go beyond the class of left-orderable groups as well. Based on a joint work with Markus Steenbock.
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- Topology Seminar