Polinomske invariante vozlov

magistrsko delo

Urša Šega (Author), Boštjan Gabrovšek (Mentor), Matija Cencelj (Co-mentor)

Abstract

V magistrskem delu, ki sodi na področje teorije vozlov, se bomo ukvarjali s problemom določanja ekvivalentnosti vozlov, natančneje s polinomskimi invariantami vozlov, ki vozlu priredijo neki vozelni polinom. S pomočjo različnih premenjalnih relacij in zvitosti bomo definirali naslednje polinomske invariante, ki nam pomagajo odgovoriti na vprašanje o ekvivalentnosti vozlov: Alexandrov polinom, Alexander-Conwayjev polinom, Jonesov polinom, Kauffmanov polinom F, Kauffmanov oklepaj, Kauffmanov polinom X in HOMFLY-PT polinom. Za vsako izmed definiranih polinomskih invariant bomo naredili ekspliciten izračun njene vrednosti za Hopfov splet in vozel deteljico. Nekatere izmed teh invariant v literaturi veljajo za močnejše invariante (HOMFLY-PT polinom, Kauffmanov polinom F) in prepoznajo več vozlov, druge pa veljajo za nekoliko šibkejše. V magistrskem delu bomo te domneve dokazali in poiskali relacije med definiranimi polinomskimi invariantami vozlov.

Keywords

polinomska invarianta vozla;Alexandrov polinom;Alexander-Conwayjev polinom;Jonesov polinom;Kauffmanov polinom;Kauffmanov oklepaj;HOMFLY-PT polinom;teorije vozlov;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[U. Šega]
UDC:	51(043.2)
COBISS:	12505417
Views:	522
Downloads:	85
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Polynomial invariants of knots
Secondary abstract:	In this MSc thesis, which deals with certain topics from knot theory, we will engage with the problem of determining knot equivalences. More accurately, with polynomial invariants of knots, which map knots to certain polynomials. With the aid of various skein relations and the writhe, we will define the following polynomial invariants, which will help us determine which knots are equivalent: Alexander polynomial, Alexander-Conway polynomial, Jones polynomial, Kauffman polynomial F, bracket polynomial, Kauffman polynomial X and HOMFLY-PT polynomial. For every defined polynomial invariant, we will explicity compute its value for the Hopf link and the trefoil knot. Some of these invariants dominate other invariants (HOMFLY-PT and Kauffman polynomial F), which means that they can distinguish between more knots than other invariants. In this MSc thesis we will prove this preposition and find a complete set of relations between the defined polynomial invariants of knots.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Predmetno poučevanje
Pages:	49 str.
ID:	11186335