Tyrone Ghaswala, University of Manitoba
"Amalgamated free products of circularly ordered groups"
Circularly ordered groups rear their heads in dynamical systems and 3-manifold topology. Motivated by problems in 3-manifold topology, it is natural to ask the following question: When is it possible to circularly order an amalgamated free product of circularly ordered groups with an order extending that on each of the factors? Since amalgamated free products in group theory are colimits in the category of groups, we address the question by studying the category of circularly ordered groups. Unfortunately, this category does not admit the desired colimits. To get around this, we embed the category of circularly ordered groups in a larger category that admits the desired colimits, and obtain some surprising results along the way. I will not assume any familiarity with circularly ordered groups.
This is joint work with Adam Clay.