Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics
type: Item
instance of: scholarly article
title: Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics
zbMATH Open document ID: 1024.81055
DOI: 10.1016/S0960-0779(01)00242-9
published in: Chaos, Solitons and Fractals
publication date: 2002-08-18T00:00:00Z
review text: The author of this interesting paper presents unsuspected connections between topology, geometry and abstract algebra on the one hand and high-energy particle physics on the other. It is shown that wildly embedded knot-like structures are variants of the \(\mathcal E\)\(^{\infty }\) theory and that they are deeply connected with hyperbolic geometry, four-dimensional fusion algebra, von Neumann-Connes geometry, Penrose spaces and Freedman theory of four manifolds. The paper is a perfect description of the wild topology. Coloured figures give a clear notion to the wild topology and how the topology is connected with geometry, abstract algebra and high-energy particle physics.
Mathematics Subject Classification ID: 81V35
Mathematics Subject Classification ID: 81T75
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 81R15
zbMATH DE Number: 1783197
zbMATH Keywords: high energy particle
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: fusion algebra
zbMATH Keywords: quantum gravity
zbMATH Keywords: knot-like structures
zbMATH Keywords: \({\mathcal E}^\infty\) theory
zbMATH Keywords: von Neumann-connes geometry
zbMATH Keywords: Penrose spaces
zbMATH Keywords: Freedman theory of four manifolds
author: Mohamed Saladin El Naschie
reviewed by: Dimitar A. Kolev
MaRDI profile type: Publication
cites work: A homogeneous indecomposable plane continuum
cites work: Q3747346
cites work: Q4417654
cites work: On Knots. (AM-115)
cites work: Superstrings, knots, and noncommutative geometry in \({\mathcal E}^{(\infty)}\) space
cites work: A general theory for the topology of transfinite heterotic strings and quantum gravity
cites work: The exact value of the smallest quantum gravity coupling constant is \(1/\alpha_{g}=42. 36067977\)
cites work: Quantum loops, wild topology and fat Cantor sets in transfinite high-energy physics
cites work: Q4314293
cites work: Topological quantum field theories derived from the Kauffman bracket
cites work: Q3472677
cites work: Q4338929
cites work: Q5557964
cites work: Q4730462
cites work: Q4040346
description: scientific article; zbMATH DE number 1783197