The minimum crossing number of essential tangles
arXiv:1505.07268 · doi:10.1142/S0218216514500540; 10.1142/S0218216517920018
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.
16 pages, 20 figures; In this version we correct three arguments on the proofs of the tangles of Theorems 1.1 and 1.2 being essential. The results of the original paper remain unaltered