Fibered Ribbon Knots vs. Major 4D Conjectures - Part 1

Explore a mathematical lecture that delves into the relationship between fibered ribbon knots and the smooth 4D Poincaré conjecture. Learn about the fundamental concepts of fibered knots, which are characterized by their complement in S^3 forming a bundle space over a circle, and ribbon knots that bound smooth disks in B^4 without local maxima in radial height. Examine the significant implications of Casson-Gordon's 1983 theorem, which suggests that fibered ribbon knots without fibered disk boundaries in B^4 could potentially disprove the smooth 4D Poincaré conjecture. Discover the criteria for extending fibrations and understand why many ribbon disks bounded by fibered knots are themselves fibered, while considering the ongoing search for non-fibered examples in this advanced topology discussion.