A topological view of ordered groups
Volume 103 / 2014
Banach Center Publications 103 (2014), 357-369
MSC: 20F60.
DOI: 10.4064/bc103-0-13
Abstract
In this expository article we use topological ideas, notably compactness, to establish certain basic properties of orderable groups. Many of the properties we shall discuss are well-known, but I believe some of the proofs are new. These will be used, in turn, to prove some orderability results, including the left-orderability of the group of PL homeomorphisms of a surface with boundary, which are fixed on at least one boundary component.
