Mezglu teorija: mezglu invarianti un to pielietojumi

Abstract

Darbā ir dots mezglu teorijas pamatjēdzienu un problemātikas apraksts. Īpaša uzmanība veltīta mezglu ekvivalences noteikšanai. Aprakstīti mezglu invarianti – iekrāsošana, iekavu polinoms, Džonsa polinoms, Aleksandra polinoms un Konvaja polinoms. Šie invarianti ilustrēti ar piemēriem. Dots ieskats kā mezglu teorijas elementi pielietojami bioķīmijā, DNS pētījumos.

The paper gives the basic concepts and problematic description of the knot theory. Particular attention is given to the knot equivalence determination. There are described the knot invariants – tricolorability, bracket polynomial, Jones polynomial, Alexander polynomial and Conway polynomial. These invariants are illustrated by examples. There is given an insight how the knot theory is applicable in the biochemistry, in the DNA studies.