Mathematics – Group Theory
Scientific paper
2008-12-12
Mathematics
Group Theory
15 pages
Scientific paper
Let G be a left orderable group and LO(G) the space of all left orderings. We investigate the circumstances under which a left ordering < of G can correspond to an isolated point in LO(G), in particular we extend known results to cover the case of uncountable groups. With minor technical restrictions on the group G, we also find that no dense left ordering is isolated in LO(G), and that the closure of the set of all dense left orderings of G yields a dense G-delta set within a Cantor set of left orderings in LO(G). Lastly, we show that certain conditions on a discrete left ordering of G can guarantee that it is not isolated in LO(G), and we illustrate these ideas using the Dehornoy ordering of the braid groups.
No associations
LandOfFree
Isolated points in the space of left orderings of a group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Isolated points in the space of left orderings of a group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isolated points in the space of left orderings of a group will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-193303