The authors construct infinite families of knots and virtual knots where any two members are one region crossing change or arc shift move apart, proving arbitrarily high-dimensional simplexes exist in both Gordian complexes.
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Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves
The authors construct infinite families of knots and virtual knots where any two members are one region crossing change or arc shift move apart, proving arbitrarily high-dimensional simplexes exist in both Gordian complexes.