The Gordian complex of knots is a simplicial complex whose vertices consist of all knot types in $𝕊^{3}$ . Local moves play an important role in defining knot invariants. There are many local moves known as unknotting operations for knots. In this paper, we discuss the 4-move operation. We show that for any knot $K_{0}$ and for any given natural number $n$ , there exists a family of knots ${K_{0}, K_{1}, \dots, K_{n}}$ such that for any pair $(K_{i}, K_{j})$ of distinct elements of the family, the Gordian distance of knots by 4-move is $d_{f} (K_{i}, K_{j}) = 1$ . We also show the existence of an arbitrarily high dimensional simplex in the Gordian complexes.

Keywords:

AMSC: 57K10, 57K14

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