Virtual knots and parity of crossings
报告题目(Title)：Virtual knots and parity of crossings
报告人(Speaker)：Seongjeong Kim (Jilin University)
地点(Place)：后主楼1220
时间(Time)：2023年4月21日 16:00-17:00
邀请人(Inviter)：田垠
报告摘要
Virtual knot theory is one of generalizations of knot theory. In virtual knot theory virtual knots and links can be considered as circles smoothly embedded in thickened surfaces or diagrams on oriented surfaces. One can expect that virtual knots has geometric properties derived from thickened surfaces, where the given virtual knot is placed.
One of important tools to study virtual knots is the parity. By using parity it is possible to construct invariants for virtual knots by using classical knot invariant. Moreover, it is known that the parity is closely related to the homology group of the underlying surface of the given virtual knot.
In this talk, we will introduce basic definitions and theorems for virtual knot theory and talk about the motivation and applications of parity.
