Geometry and Topology Seminar —— Changing the Geometry of Knots by Full Twists on Braids
报告人：Thiago de Paiva（北京国际数学研究中心）
时间：2025-11-05 15:10-17:00
地点：智华楼四元厅（225）
【摘要】
We study how the geometric type of a knot, given by the closure of a braid, changes under the addition of full twists. From a geometric viewpoint, this operation corresponds to performing specific Dehn fillings along the braid axis. We provide a complete characterization of the resulting knot type—torus, satellite, or hyperbolic—in terms of the geometry of the original closure. This description clarifies the relationship between full-twist braid operations and the geometric transformations they induce. As an application, we classify the geometric types of all twisted torus knots T(p, q; r, s) with s>1, thereby resolving the remaining open case s = 1, up to one exceptional family. This is a joint work with Professor Yi Liu.
