Introduction to Circular Orderings - Lecture 1

Embark on a comprehensive algebraic and combinatorial exploration of circularly-orderable groups in this 54-minute lecture by Tyrone Ghaswala. Delve into fundamental definitions and examine how circular orderability interacts with basic group operations such as subgroups, extensions, products, and quotients. Investigate the role of second cohomology, both bounded and unbounded, and its connection to left-ordered central extensions of circularly-ordered groups. Analyze the relationships between cohomology class properties, circular ordering characteristics, and group attributes. Conclude with an insightful discussion on obstruction spectra of circularly-orderable groups and direct products. Engage with challenging exercises, including open problems, throughout the lecture. While some interplay with Adam Clay's minicourse on left-orderability is present, this self-contained presentation offers a solid foundation in circular orderings.