Corpus ID: 199442620

# The tunnel number of all 11 and 12 crossing alternating knots

@article{CastellanoMacias2019TheTN,
title={The tunnel number of all 11 and 12 crossing alternating knots},
journal={arXiv: Geometric Topology},
year={2019}
}
• Published 5 August 2019
• Mathematics
• arXiv: Geometric Topology
Using exhaustive techniques and results from Lackenby and many others, we compute the tunnel number of all 1655 alternating 11 and 12 crossing knots. We also use these methods to compute the tunnel number of 142 non-alternating 11 and 12 crossing knots. Overall, of the 2728 total knots with 11 and 12 crossings, we have found 1797 tunnel numbers.

#### References

SHOWING 1-10 OF 41 REFERENCES
Examples of tunnel number one knots which have the property ‘1 + 1 = 3’
• Mathematics
• 1996
Let K be a knot in the 3-sphere S 3 , N ( K ) the regular neighbourhood of K and E ( K ) = cl(S 3 − N ( K )) the exterior of K . The tunnel number t ( K ) is the minimum number of mutually disjointExpand
Classification of Alternating Knots with Tunnel Number One
An alternating diagram encodes a lot of information about a knot. For example, if an alternating knot is composite, this is evident from the diagram [10]. Also, its genus ([3], [12]) and its crossingExpand
Bridge spectra of iterated torus knots
We determine the set of all genus g bridge numbers of many iterated torus knots, listing these numbers in a sequence called the bridge spectrum. In addition, we prove a structural lemma about theExpand
On the classification of rational tangles
• Mathematics, Computer Science
• 2004
Two new combinatorial proofs of the classification of rational tangles using the calculus of continued fractions are given and an elementary proof that alternatingrational tangles have minimal number of crossings is obtained. Expand
Jones polynomials and classical conjectures in knot theory
The primeness is necessary in the last statement ofTheorem B, since the connected sum of two figure eight knots is alternating, but it has a minimal non-alternating projection. Note that the figureExpand
Knots
• David M. Jackson
• CMS Books in Mathematics
• 2019
As indicated by the table of contents, Sections 2 and 3 constitute a start on the subject of knots. Later sections introduce more technical topics. The theme of a relationship of knots with physicsExpand
A spanning tree expansion of the jones polynomial
A NEW combinatorial formulation of the Jones polynomial of a link is used to establish some basic properties of this polynomial. A striking consequence of these properties is the result that a linkExpand
The Heegaard genus of manifolds obtained by surgery on links and knots
Let L⊂S3 be a fixed link. It is shown that there exists an upper bound on the Heegaard genus of any manifold obtained by surgery on L. The tunnel number of L, T(L), is defined and used as an upperExpand
Wirtinger systems of generators of knot groups
• Mathematics
• 2017
We define the {\it Wirtinger number} of a link, an invariant closely related to the meridional rank. The Wirtinger number is the minimum number of generators of the fundamental group of the linkExpand