21 citations · 82 across the 22 of their papers we have counts for
15 papers · 1 filter
The number of locally invariant orderings of a group
Idrissa Ba, Adam Clay, Ian Thompson
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we prov…
The space of circular orderings and semiconjugacy
Adam Clay, Idrissa Ba
Work of Linnell shows that the space of left-orderings of a group is either finite or uncountable, and in the case that the space is finite, the isomorphism type of the group is kn…
Circularly ordering direct products and the obstruction to left-orderability
Adam Clay, Tyrone Ghaswala
Motivated by the recent result that left-orderability of a group is intimately connected to circular orderability of direct products , we provi…
Borel structures on the space of left-orderings
Filippo Calderoni, Adam Clay
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 s…
Dense orderings in the space of left-orderings of a group
Adam Clay, Tessa Reimer
Every left-invariant ordering of a group is either discrete, meaning there is a least element greater than the identity, or dense. Corresponding to this dichotomy, the spaces of le…
Promoting circular-orderability to left-orderability
Jason Bell, Adam Clay, Tyrone Ghaswala
Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A…