We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples of isolated orderings, and give an example of isolated left orderings with various properties which previously known isolated orderings do not have.
"Construction of isolated left orderings via partially central cyclic amalgamation." Tohoku Math. J. (2) 68 (1) 49 - 71, 2016. https://doi.org/10.2748/tmj/1458248862