Symmetric Unions and Ribbon Knots
Explore the intricacies of symmetric unions and ribbon knots in this comprehensive lecture by Feride Ceren Kose from the University of Georgia. Delve into the classical construction of symmetric unions introduced by Kinoshita and Terasaka in the 1950s, examining their flexibility and prevalence in knot theory literature. Investigate the ongoing question of whether all ribbon knots can be presented as symmetric unions, drawing parallels to the Slice-Ribbon conjecture. Learn about the classification of the simplest types of symmetric unions, including composite, two-bridge, Montesinos, and amphichiral knots. Discover infinite families of ribbon knots that cannot be represented by the simplest symmetric union diagrams. Cover key concepts such as basic definitions, boundary ribbon knots, metric unions, cone raise, and partial ribbon knots, concluding with a discussion on related questions in the field.