School Colloquium——On fibered knots with fixed-point-free monodromies
报告人：程哲驰 (武汉大学)
时间：2025-10-10 14:00-15:00
地点：智华楼四元厅
报告摘要：A fibered knot in the 3-sphere is one whose complement is a surface bundle over the circle. The topology of this bundle is determined by its fiber surface and the associated monodromy. The dynamics of this monodromy map, particularly its fixed-point set, are central to understanding the geometry of the knot complement.
In this talk, we start with surveying classical results on fibered knots, including a celebrated theorem by Stallings in the 70s which shows that positive braids are always fibered. We will then introduce the powerful modern tool of Heegaard Floer homology and explain how it governs the fiberedness of the knot and its monodromy. Finally, we show that every prime positive braid knot admits a fixed-point-free monodromy. This is joint work with Matthew Hedden.
报告人简介：Zhechi Cheng is an associate researcher at Wuhan University. He received his Ph.D. in Mathematics from Columbia University under the supervision of Professor Mohammed Abouzaid, following his undergraduate studies at Peking University. His research focuses on symplectic geometry and its interactions with low-dimensional topology. Specific interests include Heegaard Floer homology and symplectic Khovanov homology. His work has been published in leading journals in the field, including Quantum Topology and Algebraic & Geometric Topology.
