Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants

Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants Full article

Journal

Journal of Knot Theory and its Ramifications
ISSN: 0218-2165

Output data

Year: 2018, Volume: 27, Number: 13, Article number : 1842015, Pages count : DOI: 10.1142/S0218216518420154

Tags

affine index polynomial; cosmetic crossing change; Virtual knot

Authors

Kaur K. ¹ , Prabhakar M. ¹ , Vesnin A. ^2,3

Affiliations

1	Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001, India
2	Tomsk State University, Tomsk, 634050, Russian Federation
3	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation

We introduce two sequences of two-variable polynomials Ln K (t, ℓ)}∞ n=1 and n K (t, ℓ)}∞ n=1, expressed in terms of index value of a crossing and n-dwrithe value of a virtual knot K, where t and l are variables. Basing on the fact that n-dwrithe is a flat virtual knot invariant, we prove that LKn and FKn are virtual knot invariants containing Kauffman affine index polynomial as a particular case. Using LK n we give sufficient conditions when virtual knot does not admit cosmetic crossing change. © 2018 World Scientific Publishing Company.

Kaur K. , Prabhakar M. , Vesnin A.
Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants
Journal of Knot Theory and its Ramifications. 2018. V.27. N13. 1842015 . DOI: 10.1142/S0218216518420154 WOS Scopus OpenAlex

Web of science:	WOS:000454309600010
Scopus:	2-s2.0-85057766451
OpenAlex:	W2964348242

DB	Citing
Scopus	16
OpenAlex	21
Web of science	14