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Explore the algebraic and combinatorial foundations of circularly-orderable groups in this comprehensive lecture. Delve into the relationship between cohomology classes and circular ordering properties, examining how circular orderability interacts with fundamental group operations. Investigate the left-ordered central extension of circularly-ordered groups and analyze the obstruction spectrum. Engage with challenging exercises, including open problems, to deepen understanding of these advanced mathematical concepts. While some interplay with left-orderability is present, the majority of the content stands independently, providing a rigorous exploration of circular orderings in group theory.
