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ON THE SATELLITE CROSSING NUMBER CONJECTURE

A. STOIMENOW

Department of Mathematics, Keimyung University, Dalseo-Gu, Sindang-Dong 1000, Daegu 704-701, Korea

https://doi.org/10.1142/S1793525311000568Cited by:3 (Source: Crossref)

Abstract

We prove some estimates on the crossing number of satellites of adequate, and partly of semiadequate knots. We mostly deal with classical cables, obtaining the first examples where the asymptotic cable crossing number is shown to be equal to the companion crossing number. Our approach can also be applied to Whitehead and Bing doubles and positive braid cables. For some patterns one can use it to determine their geometric degree.

Keywords:

AMSC: 57M25

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