2008/12/12 by Adam Clay, Clay, Adam · 1 citation
Mathematics · #20F60 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20F60
paper · pdf · doi:10.48550/arxiv.0812.2499
15 pages
arxiv created 2008/12/12 · openalex publication_date 2008/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.