Knot Floer Homology: A Bridge Connecting Topology, Symplectic Geometry, and Combinatorics

：陈兆君（美国加州理工大学）
：2025-08-15 10:00
：海韵园行政楼C503

报告人：陈兆君（美国加州理工大学）

时  间：2025年8月15日10:00

地  点：海韵园行政楼C503

内容摘要:

In this talk, we explore knot Floer homology (HFK), a powerful combinatorial and homological invariant for knots in the 3-sphere. Developed by Ozsváth and Szabó, HFK associates a bigraded vector space to a knot, refining fundamental invariants like the Alexander polynomial and the knot genus. We outline the foundational ideas behind HFK, including its construction via Heegaard diagrams or grid diagrams. We also examine key properties of HFK, such as its role in detecting the Seifert genus and fiberedness of knots. Furthermore, we discuss its relationship to the three-genus, slice genus, and the broader landscape of knot concordance. Finally, we touch upon the computational aspects and significance of HFK in modern low-dimensional topology.

个人简介：

陈兆君，美国加州理工大学博士研究生，师从倪忆教授。主要研究兴趣包括纽结理论，Floer同调及其在四维拓扑中的应用等。

 

联系人：杨璟玲