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Recurrent Generalization of F-Polynomials for Virtual Knots and Links
Amrendra Gill, Maxim Ivanov, Madeti Prabhakar +1
F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman's affine inde…
An unknotting invariant for welded knots
K. Kaur, A. Gill, M. Prabhakar +1
We study a local twist move on welded knots that is an analog of the virtualization move on virtual knots. Since this move is an unknotting operation we define an invariant, unknot…
A characteristics for a surface sum of two handlebodies along an annulus or a once-punctured torus to be a handlebody
Fengchun Lei, He Liu, Fengling Li +1
The main results of the paper is that we give a characteristics for an annulus sum and a once-punctured torus sum of two handlebodies to be a handlebody as follows: 1. The annulus…
Polynomials of genus one prime knots of complexity at most five
Maxim Ivanov, Andrei Vesnin
Prime knots of genus one admitting diagram with at most five classical crossings were classified by Akimova and Matveev in 2014. In 2018 Kaur, Prabhakar and Vesnin introduced famil…
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves
Amrendra Gill, Madeti Prabhakar, Andrei Vesnin
Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in . Later Horiuchi and Ohyama defined G…
-polynomials of tabulated virtual knots
Maxim Ivanov, Andrei Vesnin
A sequence of -polynomials of virtual knots was defined by Kaur, Prabhakar, and Vesnin in 2018. These polynomials have been expressed i…