Orderable groups and their computability properties

Arman Darbinyan (U of Vienna)

Jul 17. 2023, 14:50 — 15:30

An important class of groups is the one that consists of groups admitting linear orders invariant under left (and right) multiplication. For groups in this class, it is natural to ask how complex (or not complex) can the (left) orders on them be. As a measure of such complexity, one can consider computability properties of the orders. In particular, an old question of Downey and Kurtz asks if every bi-orderable group that has decidable word problem admits computable bi-order. In my talk, I will describe a class of bi-orderable groups with decidable word problems that do not admit any computable left- and bi- orders in a strong sense; namely, they even do not embed into any group with a computable left-order.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics (Workshop)
Christopher Cashen (U of Vienna)
Javier de la Nuez González (KIAS, Seoul)
Alexandra Edletzberger (U of Vienna)
Yash Lodha (U of Hawaii, Honolulu)