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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-13,
author = {Dale Rolfsen},
title = {A topological view of ordered groups},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {357-369},
zbl = {1316.06020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-13}
}
Dale Rolfsen. A topological view of ordered groups. Banach Center Publications, Tome 102 (2014) pp. 357-369. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc103-0-13/