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ON A BALL IN A METRIC SPACE OF KNOTS BY DELTA MOVES

SUMIKO HORIUCHI

Department of Mathematics, College of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo, 167-8585, Japan

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https://doi.org/10.1142/S0218216508006361Cited by:1 (Source: Crossref)

Abstract

We consider the metric space of all knots on which the distance is defined by delta moves. We show that for any two knots K₁ and K₂ with delta distance k and for any natural numbers ℓ and m with ℓ + m = k, the intersection of the ball of radius ℓ centered at K₁ and the ball of radius m centered at K₂ contains infinitely many knots. We also consider the problem whether or not the center of a given ball is unique.

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AMSC: 57M25

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