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The generalized Yamada polynomial of virtual spatial graphs
发布时间: 2018-10-07     20:31   【返回上一页】 发布人:金贤安


 北京师范大学数学科学学院

 

周五公众报告

 

 

报告题目:The generalized Yamada polynomial of virtual spatial graphs

 

报告人:金贤安教授(厦门大学)

 

时间地点:10月12日16:00-17:00, 后主楼1124

 

邀请人:程志云

 

报告摘要:Knot theory can be generalized to virtual knot theory and spatial graph theory. In 2007, Fleming and Mellor combined and generalized them to virtual spatial graph theory in a combinatorial way. The main goal is to generalize the classical Yamada polynomial for spatial graphs. We shall define the generalized Yamada polynomial for virtual spatial graphs via their diagrams and prove that it can be normalized to be a rigid vertex isotopic invariant of virtual spatial graphs and to be a pliable vertex isotopic invariant for virtual spatial graphs with maximum degree at most 3. We also consider the connection and difference between the generalized Yamada polynomial and the Dubrovnik polynomial of a classical link. That is, the generalized Yamada polynomial specializes to a version of the Dubrovnik polynomial for classical links such that it can be used to sometimes detect the non-classicality of virtual links. As an application of the generalized Yamada polynomial, via the Jones-Wenzl projector $P_2$ acting on a virtual spatial graph diagram,we get a specialization for the generalized Yamada polynomial, which can be used to write a program for calculating the generalized Yamada polynomial based on Mathematica code.

 This is joint work with Qingying Deng and Louis H. Kauffman.

 

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