Low Dimensional Topology and Circle-valued Morse Functions

Explore a fascinating lecture on low-dimensional topology and circle-valued Morse functions presented by Alex Zupan from the University of Nebraska-Lincoln. Delve into an extension of the Casson-Gordon theorem, which originally applied to fibered knots in the 3-sphere. Learn how this result is expanded to non-fibered knots, introducing the concept of handle-ribbon knots. Discover the relationship between singular fibrations, determined by circular Morse functions, and the extension of knot exteriors over handlebodies. Gain insights into the conditions between ribbonness and sliceness in knot theory, and understand the significance of closed monodromy in this context. This hour-long talk, part of a conference at the University of Miami, presents joint work with Maggie Miller, offering a deep dive into advanced concepts in low-dimensional topology.