Low Dimensional Topology and Circle-Valued Morse Functions

Explore a cutting-edge lecture on low-dimensional topology and circle-valued Morse functions presented by Ian Agol from UC Berkeley. Delve into the intricacies of knot complements and their decomposition along maximal collections of disjoint minimal genus Seifert surfaces. Learn about the process of removing product bundles by cutting along product annuli and discover the groundbreaking proof that the resulting sutured manifold is unique up to isotopy, regardless of the chosen Seifert surfaces. Examine the implications of this finding on the dimension of maximal simplices in the Kakimuzu complex. Investigate the extension of this result to Thurston norm-minimizing surfaces realizing second homology classes in certain 3-manifolds. Gain insights into the collaborative research conducted with Yue Zhang in this hour-long exploration of advanced mathematical concepts in topology.