arXiv subjects
Publications and source records attributed to Charilaos Aneziris.
While the problem of knot classification is far from solved, it is possible to create computer programs that can be used to tabulate knots up to a desired degree of complexity. Here we discuss the main ideas on which such programs can be based. We also present the actual results obtained after running a computer program on which knots are denoted through regular projections.
In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.
I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical aspects related to running these algorithms as computer programs. Further on, we reach a solution by improving on the efficiency of these algorithms, and by introducing new ones.
The goal of this paper is to discuss the possibility of finding an algorithm that can give all distinct knots up to a desired complexity. Two such algorithms are presented, one based on projections on a plane, the other on closed self-avoiding walks.
We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on placing knots on a cubic lattice.