Mutation invariance of the arc index for some Montesinos knots

2017/04/06 by Jin, Gyo Taek, Lee, Ho
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1704.01787

Abstract

For the alternating knots or links, mutations do not change the arc index. In the case of nonalternating knots, some semi-alternating knots or links have this property. We mainly focus on the problem of mutation invariance of the arc index for nonalternating knots which are not semi-alternating. In this paper, we found families of infinitely many mutant pairs/triples of Montesinos knots with the same arc index.

Related

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• Prime knots whose arc index is smaller than the crossing number
• Mutation and the colored Jones polynomial
• Prime knots with arc index up to 11 and an upper bound of arc index for\n non-alternating knots
• Characterization of Quasi-alternating Montesinos Links