A note on coverings of virtual knots

2018/11/27 by Nakamura, Takuji, Nakanishi, Yasutaka, Satoh, Shin
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1811.10852

Abstract

For a virtual knot K and an integer r≥ 0, the r-covering K^(r) is defined by using the indices of chords on a Gauss diagram of K. In this paper, we prove that for any finite set of virtual knots J₀,J₂,J₃,…,J_m, there is a virtual knot K such that K^(r)=J_r (r=0 and 2≤ r≤ m), K⁽¹⁾=K, and otherwise K^(r)=J₀.

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