Low Dimensional Topology and Circle-valued Morse Functions

Explore a 59-minute conference talk on forbidden minor multibranched surfaces and critical complexes in low-dimensional topology. Delve into the research presented by Makoto Ozawa from Komazawa University, focusing on the $K_5 \times S^1$ and $K_{3,3} \times S^1$ families as forbidden minors for multibranched surfaces embeddable in the 3-sphere $S^3$. Examine the concept of critical complexes and their relationship to forbidden minors. Investigate the classification of critical complexes in the form $(G\times S^1)\cup H$, where $G$ and $H$ are graphs. Learn about the partially ordered set of complexes that arises from these examples and its properties. Gain insights into this joint work with Mario Eudave-Muñoz, presented as part of the Low Dimensional Topology & Circle-valued Morse Functions conference at the University of Miami.