E-infinity Cantorian space-time from subfactors and knot theory

Abstract

Najprej podamo nekaj definicij in izrekov o subfaktorjih in o Jonesovem indeksu. Vzpostavimo povezavo med Jonesovim indeksom in geometrijo 4-mnogoterosti. Pokažemo, da velja relacija kit samo takrat, ko sta parametra ▫$\taut$▫ in ▫$q \in \{e^\frac{2\pi}{n}, n=3,4,...\} \cup (0,\infty)$▫ povezana z Jonesovo enačbo ▫$\tau^{-1} = q + q^{-1} + 2$▫. Pokažemo, da invarianta ▫$V_L$▫ orientiranih spletov opisuje vozle v E-neskončno Cantorjevem prostoru-času. Z drugimi besedami, E-neskončno Cantorjev prostor-čas je možno konstruirati z uporabo teorije subfaktorjev in teorije vozlov.

Keywords

E-neskončno Cantorjev prostor-čas;subfaktorji;Jonesov indeks;E-infinity Cantorian space-time;subfactors;Jones' indeks;

Data

Language:	English
Year of publishing:	2007
Typology:	1.01 - Original Scientific Article
Organization:	UM FS - Faculty of Mechanical Engineering
UDC:	515.162.8:517.98
COBISS:	11021334
ISSN:	0960-0779
Views:	890
Downloads:	87
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	E-neskončno Cantorjev prostor-čas od subfaktorjev in teorije vozlov
Secondary abstract:	First we give some definitions and theorems about subfactors and Jones' index. Subsequently the connection between Jonesć index and the geometry of four manifolds is outlined. It is shown that the braid relation can be satisfied only when the parameters ▫$\taut$▫ and ▫$q \in \{e^\frac{2\pi}{n}, n=3,4,...\} \cup (0,\infty)$▫ are related by Jones' equation ▫$\tau^{-1} = q + q^{-1} + 2$▫. The invariant ▫$V_L$▫ of oriented links is shown to describe knots in E-infinity Cantorian space-time. In other words E-infinity may be constructed using the mathematics of subfactors and knot theory.
Secondary keywords:	matematika;
URN:	URN:SI:UM:
Pages:	str. 916-919
Volume:	ǂVol. ǂ32
Issue:	ǂiss. ǂ3
Chronology:	2007
ID:	8718638