The minimum crossing number of essential tangles

João Miguel Nogueira; António Salgueiro

doi:10.1142/s0218216514500540; 10.1142/s0218216517920018

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arXiv · 1505.07268

The minimum crossing number of essential tangles

João Miguel Nogueira·António Salgueiro

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Abstract

In this paper we compute the sharp lower bounds for the crossing number of $n$-string $k$-loop essential tangles. For essential tangles with only string components, we characterise the ones with the minimum crossing number for a given number of components, both when the tangle has knotted strings or only unknotted strings.

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João Miguel Nogueira, António Salgueiro. 2017-08-29. The minimum crossing number of essential tangles. https://doi.org/10.1142/s0218216514500540%3B%2010.1142%2Fs0218216517920018

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