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- catalog abstract ""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 problem 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 thorough numerical experiments."--Jacket.".
- catalog contributor b13022483.
- catalog created "c2003.".
- catalog date "2003".
- catalog date "c2003.".
- catalog dateCopyrighted "c2003.".
- catalog description ""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 problem 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 thorough numerical experiments."--Jacket.".
- catalog description "Ch. 12. The conformal sin energy E[subscript sin [theta]] -- Ch. 13. Measure of non-trivial spheres -- App. A. Generalization of the Gauss formula for the linking number -- App. B. The 3-tuple map to the set of circles in S[superscript 3] -- App. C. Conformal moduli of a solid torus -- App. D. Kirchhoff elastica -- App. E. Open problems and dreams.".
- catalog description "Includes bibliographical references (p. 271-284) and index.".
- catalog description "pt. 1. In search of the "optimal embedding" of a knot -- Ch. 1. Introduction -- Ch. 2. [alpha]-energy functional E([superscript [alpha]]) -- Ch. 3. On E([superscript 2]) -- Ch. 4. L[superscript p] norm energy with higher index -- Ch. 5. Numerical experiments -- Ch. 6. Stereo pictures of E([superscript 2]) minimizers -- Ch. 7. Energy of knots in a Riemannian manifold -- Ch. 8. Physical knot energies -- pt. 2. Energy of knots from a conformal geometric viewpoint -- Ch. 9. Preparation from conformal geometry -- Ch. 10. The space of non-trivial spheres of a knot -- Ch. 11. The infinitesimal cross ratio.".
- catalog extent "xiv, 288 p. :".
- catalog identifier "9812383166 (alk. paper)".
- catalog isPartOf "K & E series on knots and everything ; v. 33".
- catalog issued "2003".
- catalog issued "c2003.".
- catalog language "eng".
- catalog publisher "River Edge, NJ : World Scientific Pub.,".
- catalog subject "514/.224 21".
- catalog subject "Conformal geometry.".
- catalog subject "Knot theory.".
- catalog subject "QA612.2 .O36 2003".
- catalog tableOfContents "Ch. 12. The conformal sin energy E[subscript sin [theta]] -- Ch. 13. Measure of non-trivial spheres -- App. A. Generalization of the Gauss formula for the linking number -- App. B. The 3-tuple map to the set of circles in S[superscript 3] -- App. C. Conformal moduli of a solid torus -- App. D. Kirchhoff elastica -- App. E. Open problems and dreams.".
- catalog tableOfContents "pt. 1. In search of the "optimal embedding" of a knot -- Ch. 1. Introduction -- Ch. 2. [alpha]-energy functional E([superscript [alpha]]) -- Ch. 3. On E([superscript 2]) -- Ch. 4. L[superscript p] norm energy with higher index -- Ch. 5. Numerical experiments -- Ch. 6. Stereo pictures of E([superscript 2]) minimizers -- Ch. 7. Energy of knots in a Riemannian manifold -- Ch. 8. Physical knot energies -- pt. 2. Energy of knots from a conformal geometric viewpoint -- Ch. 9. Preparation from conformal geometry -- Ch. 10. The space of non-trivial spheres of a knot -- Ch. 11. The infinitesimal cross ratio.".
- catalog title "Energy of knots and conformal geometry / Jun O'Hara.".
- catalog type "text".