Author： Gamkrelidze A.
Publisher： Springer Publishing Company
ISSN： 1072-3374
Source： Journal of Mathematical Sciences, Vol.195, Iss.2, 2013-11, pp. : 139-145
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
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.
Related content
Symplectic convexity in low-dimensional topology
By Etnyre J.B.
Topology and its Applications, Vol. 88, Iss. 1, 1998-10 ,pp. :
Access to resources
Recommend
INVARIANT THEORY AND THE INVARIANTS OF LOW-DIMENSIONAL TOPOLOGY
By Liu K.
Topology, Vol. 38, Iss. 4, 1999-07 ,pp. :
By Sevilla F.J. Grether M. Fortes M. de Llano M. Rojo O. Solís M.A. Valladares A.A.
Journal of Low Temperature Physics, Vol. 121, Iss. 5-6, 2000-12 ,pp. :
Applications of quantum invariants in low dimensional topology
Topology, Vol. 37, Iss. 1, 1998-01 ,pp. :
Vortices in Low-Dimensional Magnetic Systems
By Costa B.
Brazilian Journal of Physics, Vol. 41, Iss. 1, 2011-05 ,pp. :