Quandle theory and its applications to knots
数学专题报告
报告题目(Title)：Quandle theory and its applications to knots
报告人(Speaker)：Takefumi Nosaka (Institute of Science Tokyo)
地点(Place)：后主楼1124
时间(Time)：10:00-11:00, June 4, 2025
邀请人(Inviter)：Zhiyun Cheng
报告摘要
A quandle is an algebraic system analogous to the conjugacy operation of a group, and is suitable for applications in knot theory. Given a quandle X, Feen-Rourke-Sanderson defined a classifying space BX, whose cohomology is called the rack cohomology. Some topological invariants obtained from a cocycle of BX are called the quandle cocycle invariants. In this talk I will give a survey of quandle (cohomology) and BX, and demonstrate an overview of my results on quandles. For example, I gave some topological invariants (or computations of them) of cup products of knots, cohomology pairing. and closed 3-manifolds etc.
