Spaces of enumerated orderable groups

Abstract: An enumerated group is a group structure on the natural numbers. Given one among various notions of orderability of countable groups, we endow the class of orderable enumerated groups with a Polish topology. In this setting, we establish a plethora of genericity results using elementary tools from Baire category theory and the Grigorchuk space of marked groups. In this talk I will describe these spaces and some of their striking features. This is ongoing joint work with Srivatsav Kunnawalkam Elayavalli and Issac Goldbring.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away