Free products of circularly-ordered groups with amalgamated subgroup
Group Theory
2019-12-11 v2 Geometric Topology
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.
Cite
@article{arxiv.1807.08082,
title = {Free products of circularly-ordered groups with amalgamated subgroup},
author = {Adam Clay and Tyrone Ghaswala},
journal= {arXiv preprint arXiv:1807.08082},
year = {2019}
}
Comments
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)