Overview

Energy of knots is a theory that was introduced to create a ""canonical configuration"" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a ""canonical configuration"" of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments.

Full Product Details

Author:   Jun O'hara (Tokyo Metropolitan Univ, Japan)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   33
Dimensions:   Width: 16.20cm , Height: 2.40cm , Length: 23.00cm
Weight:   0.667kg
ISBN:  

9789812383167

ISBN 10:   9812383166
Pages:   304
Publication Date:   26 March 2003
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

In Search of the Optimal Embedding of a Knot: -Energy Functional E( ); On E(2); Lp Norm Energy with Higher Index; Numerical Experiments; Stereo Pictures of E(2) Minimizers; Energy of Knots in a Riemannian Manifold; Physical Knot Energies; Energy of Knots from a Conformal Geometric Viewpoint: Preparation from Conformal Geometry; The Space of Non-Trivial Spheres of a Knot; The Infinitesimal Cross Ratio; The Conformal Sin Energy Esin ; Measure of Non-Trivial Spheres; Appendices: Generalization of the Gauss Formula for the Linking Number; The 3-Tuple Map to the Set of Circles in S3; Conformal Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams.

Reviews

.,. gives an excellent, state of the art account of many of the important results in this field.

".,."" gives an excellent, state of the art account of many of the important results in this field."""

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