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GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS
Glasgow Mathematical Journal ( IF 0.5 ) Pub Date : 2020-02-03 , DOI: 10.1017/s0017089520000014 DUNCAN MCCOY
Glasgow Mathematical Journal ( IF 0.5 ) Pub Date : 2020-02-03 , DOI: 10.1017/s0017089520000014 DUNCAN MCCOY
For p ≥ 1, one can define a generalisation of the unknotting number tup called the p th untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tu p –1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large gaps between tu 1 and tu 2 .
中文翻译:
连续解捻数之间的间隙
为了p ≥ 1,可以定义解结数的一般化涂p 叫做p th untwisting number,最多统计2个null-homlogous twists的个数p 将结转换为未结所需的股线。我们证明,对于任何p ≥2 连续解捻数之差涂 p –1 和涂p 可以任意大。我们还表明,圆环结之间存在任意大的间隙涂 1 和涂 2 .
更新日期:2020-02-03
中文翻译:
连续解捻数之间的间隙
为了