Free products of circularly-ordered groups with amalgamated subgroup

Abstract

This paper gives necessary and sufficient conditions that the free product with amalgamation of circularly-ordered groups admit a circular ordering extending the given orderings of the factors. Our result follows from establishing a categorical framework that allows the problem to be restated in terms of amalgamating certain left-ordered central extensions, where we are able to apply work of Bludov and Glass.

24 pages. Minor changes made to address the referee's comments, and a complete reworking of Section 4 to strengthen the results. To appear in J. Lond. Math. Soc. (2)