报告人：金贤安 厦门大学
报告时间：7月8日 3:30-4:30
报告地点：五教 5107
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.
In this talk, we shall generalize the classical Yamada polynomial for spatial graphs to obtain the generalized Yamada polynomial for virtual spatial graphs via their diagrams. Then we prove that it can be nor-malized 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 gener-alized 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.
This is joint work with Qingying Deng and Louis H. Kauffman.
References
[1] T. Fleming, B. Mellor, Virtual spatial graphs, Kobe Journal of Mathematics, 24 (2007), 67-85.
[2] S. Yamada, An invariant of spatial graphs, Journal of Graph Theory,
13 (1989), 537-551.
[3] Q. Deng, X. Jin, L. H. Kauffman, The generalized Yamada polyno-mial of virtual spatial graphs, Topology and its Applications, 256 (2019)
136-158.
