Abstract
In this work, we reintroduce the so-called AFL (Arkaden-Faden-Lage) representation of knots introduced by Kurt Reidemeister and show how it can be used to develop efficient algorithms in low-dimensional topology. In particular, we develop an algorithm to calculate the functions for the holonomic parametrization of knots introduced by Vassiliev in 1997, who proved that each knot type has a holonomic parametrization (but no method to find such a parametrization was known). Further, we show that the result of Vassiliev can be easily derived from the AFL representation of knots. This is one of the first practical results of the application of the AFL representation of knots that can open new perspectives in the field of low dimensional topology such as computation of the Kontsevich integral and some operators of quantum groups.
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