The State-Sum Invariants for Virtual Knot

被引：0

作者：

Kazakov, A. A. ^{[1
,2
,3
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow 119991, Russia

[2] Demidov Yaroslavl State Univ, Ctr Integrable Syst, Yaroslavl 150003, Russia

[3] Moscow Inst Phys & Technol, Ctr Fundamental Math, Dolgoprudnyi 141701, Moscow Oblast, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 12期

关键词：

virtual knots; virtual links; quandle; invariant state-sum; cohomology of quandle;

D O I：

10.1134/S1995080223120181

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct the new non-trivial state-sum invariants for virtual knots and links by a generalization of the powerful Carter-Saito-Jelsovsky-Kamada-Langford theorem for classical knots. The main result of this work is based on cohomology quandle theory and colorings of virtual knot and link diagrams by quandle elements.

引用

页码：5286 / 5293

页数：8

共 50 条

[21] Skein Invariants of Links and Their State Sum Models
Kauffman, Louis H.
Lambropoulou, Sofia
SYMMETRY-BASEL, 2017, 9 (10):
[22] Knot invariants
Seifert, H
SITZUNGSBERICHTE DER PREUSSICHEN AKADEMIE DER WISSENSCHAFTEN PHYSIKALISCH-MATHEMATISCHE KLASSE, 1933, : 811 - 828
[23] A general state-sum construction of 2-dimensional topological quantum field theories with defects
Kamau-Devers, Gathoni
Jardine, Gail
Yetter, David
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (04)
[24] Invariants of knot diagrams
Hass, Joel
Nowik, Tahl
MATHEMATISCHE ANNALEN, 2008, 342 (01) : 125 - 137
[25] INVARIANTS OF KNOT COBORDISM
LEVINE, J
INVENTIONES MATHEMATICAE, 1969, 8 (02) : 98 - &
[26] ON THE VASSILIEV KNOT INVARIANTS
BARNATAN, D
TOPOLOGY, 1995, 34 (02) : 423 - 472
[27] Quantum knot invariants
Stavros Garoufalidis
Research in the Mathematical Sciences, 2018, 5
[28] Quantum knot invariants
Garoufalidis, Stavros
RESEARCH IN THE MATHEMATICAL SCIENCES, 2018, 5
[29] Invariants of knot diagrams
Joel Hass
Tahl Nowik
Mathematische Annalen, 2008, 342 : 125 - 137
[30] Regional knot invariants
Yang, Zhiqing
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (06)

← 1 2 3 4 5 →