Prof. S. Friedl PhD / Prof. Dr. C. Löh

Yash Lodha (Universität Wien), 24.06.2022. A tale of two algebraic notions: left orderability and local indicability

Abstract: Whether a countable group admits a faithful action by orientation preserving homeomorphisms on R admits a striking algebraic characterisation. Such an action exists iff the group is left orderable, i.e. it admits a total order which is invariant under group (left) multiplication. A group is said to be locally indicable if every finitely generated subgroup admits a homomorphism onto the integers. This property emerged in Higman's study of units in group rings, and has found applications in the study of various long standing open problems in group theory and topology. The goal of the talk is to understand to what extent these properties differ: and the exotic examples that lurk around the boundary.