Crossing tribes of tangles in a thickened surface
数学公众报告（120周年校庆系列第11场）
报告题目(Title)：Crossing tribes of tangles in a thickened surface
报告人(Speaker)：Igor Nikonov （Lomonosov Moscow State University）
地点(Place)：ZOOM ID: 85631113538, Code: 881470
时间(Time)：2022 年 01 月 21 日（周五） 15:00--16:00
邀请人(Inviter)：程志云
报告摘要
Crossings of knot diagrams can be divided into classes (tribes) compatible with Reidemeister moves. Tribes can be considered as localization of the notion of weak chord index introduced by M. Xu. We describe tribes of crossings for tangles in a fixed surface and show that crossings are differentiated by their component, order and homotopy types. As a consequence, we conclude that there are no nontrivial indices on diagrams of classical knots.
