Abstract
For a left-orderable group G, let LO(G) denote its space of left orderings, and F(G) the free lattice-ordered group over G. This paper establishes a connection between the topology of LO(G) and the group F(G). The main result is a correspondence between the kernels of certain maps in F(G), and the closures of orbits in LO(G) under the natural G-action. The proof of this correspondence is motivated by earlier work of McCleary, which essentially shows that isolated points in LO(G) correspond to basic elements in F(G). As an application, we will study this new correspondence between kernels and the closures of orbits to show that LO(G) is either finite or uncountable. We will also show that LO(F n ) is homeomorphic to the Cantor set, where F n is the free group on n > 1 generators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
