On Vassiliev invariants of virtual knots

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-03 DOI:10.1016/j.topol.2024.108935

Wout Moltmaker , Louis H. Kauffman

引用次数: 0

Abstract

We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in [1]. In particular, following the theory of quantum invariants we work with ‘rotational’ virtual knots. We define chord diagrams, weight systems, and give examples of Lie algebra weight systems of rotational virtual knots. We end with a discussion of extended quantum invariants, which capture information that standard quantum invariants of rotational virtuals cannot.

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论虚结的瓦西里耶夫不变式

我们讨论了虚拟结的瓦西里耶夫不变式，扩展了[1]中提出的量子虚拟结不变式理论。特别是，根据量子不变式理论，我们研究 "旋转 "虚结。我们定义了弦图、权重系统，并举例说明了旋转虚拟结的李代数权重系统。最后，我们讨论了扩展量子不变式，它捕捉了旋转虚结的标准量子不变式无法捕捉的信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.