Abstract: Gordian complex of knots was defined by Hirasawa and Uchida as the simplicial complex whose vertices are knot isotopy classes in 3. Later Horiuchi and Ohyama defined Gordian complex of virtual knots using v-move and forbidden moves. In this paper, we discuss Gordian complex of knots by region crossing change and Gordian complex of virtual knots by arc shift move. Arc shift move is a local move in the virtual knot diagram which results in reversing orientation locally between two consecutive crossings. We show the existence of an arbitrarily high-dimensional simplex in both the Gordian complexes, i.e. by region crossing change and by the arc shift move. For any given knot (respectively, virtual knot) diagram we construct an infinite family of knots (respectively, virtual knots) such that any two distinct members of the family have distance one by region crossing change (respectively, arc shift move). We show that the constructed virtual knots have the same affine index polynomial. © 2020 World Scientific Publishing Company.

Cite: Gill A. , Prabhakar M. , Vesnin A.
Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves
Journal of Knot Theory and its Ramifications. 2020. V.29. N10. 2042008 . DOI: 10.1142/S0218216520420080 WOS Scopus OpenAlex

Identifiers:

Web of science:	WOS:000603053300009
Scopus:	2-s2.0-85094661953
OpenAlex:	W3041611782

Citing:

DB	Citing
Scopus	7
OpenAlex	7
Web of science	7

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