7 research outputs found
Borel structures on the space of left-orderings
In this paper we study the Borel structure of the space of left-orderings
of a group modulo the natural conjugacy action, and by
using tools from descriptive set theory we find many examples of countable
left-orderable groups such that the quotient space is not
standard. This answers a question of Deroin, Navas, and Rivas. We also prove
that the countable Borel equivalence relation induced from the conjugacy action
of on is universal, and leverage
this result to provide many other examples of countable left-orderable groups
such that the natural -action on induces a universal
countable Borel equivalence relation.Comment: 17 pages, typos corrected. An erroneous claim in Corollary 3.5 of the
previous version was removed. The exposition of Section 4 was substantially
improve
Group actions on 1-manifolds: a list of very concrete open questions
This text focuses on actions on 1-manifolds. We present a (non exhaustive)
list of very concrete open questions in the field, each of which is discussed
in some detail and complemented with a large list of references, so that a
clear panorama on the subject arises from the lecture.Comment: 21 pages, 2 figure