A TABULATION OF PRIME KNOTS UP TO ARC INDEX 11

ARC INDEX OF PRETZEL KNOTS OF TYPE (−p, q, r)

Let D be a diagram of a knot or a link L. Suppose that there is a simple closed curve C meeting D in k distinct points which divide D into k arcs α1, α2, . . . , αk with the following properties: (1) Each αi has no self-crossing. (2) If αi crosses over αj at a crossing, then i > j and it crosses over αj at any other crossings with αj . (3) For each i, there exists an embedded disk di such that ...

Automatic Evaluation of the Links–Gould Invariant for all Prime Knots of up to 10 Crossings

This paper describes a method for the automatic evaluation of the Links– Gould two-variable polynomial link invariant (LG) for any link, given only a braid presentation. This method is currently feasible for the evaluation of LG for links for which we have a braid presentation of string index at most 5. Data are presented for the invariant, for all prime knots of up to 10 crossings and various ...

On cyclic branched coverings of prime knots

The Torelli subgroup of Out(Fn) Mladen Bestvina, Utah The group in the title is the kernel of the natural map Out(Fn) –> GLn(Z). As for the classical mapping class group counterparts (except for the work of Mess in low genus), the basic features such as the dimension and finiteness properties are unknown. I will describe an approach to an understanding to these groups that leads to a complete s...

Enumerating the Prime Alternating Knots, Part Ii

Knots which Behave Like the Prime Numbers

This paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.