ON A GENERALIZATION OF THE ALEXANDER POLYNOMIAL FOR LONG VIRTUAL KNOTS

被引：3

作者：

Afanasiev, Denis ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Chair Differential Geometry & Applicat, Moscow 119991, Russia

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2009年 / 18卷 / 10期

关键词：

Long virtual knot; minimal diagram; Alexander polynomial; virtual crossing; INVARIANTS;

D O I：

10.1142/S021821650900752X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a new invariant polynomial for long virtual knots. It is a generalization of the Alexander polynomial. We designate it as zeta by meaning an analogy with zeta-polynomial for virtual links. The degree of zeta-polynomial estimates the virtual crossing number. We describe some application of zeta-polynomial for the study of minimal long virtual diagrams with respect to the number of virtual crossings.

引用

页码：1329 / 1333

页数：5

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