Exotic Smoothness And Physics: Differential Topology And Spacetime Models

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9789810241957: Exotic Smoothness And Physics: Differential Topology And Spacetime Models
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THE RECENT REVOLUTION IN DIFFERENTIAL TOPOLOGY RELATED TO THE DISCOVERY OF NON-STANDARD ("EXOTIC") SMOOTHNESS STRUCTURES ON TOPOLOGICALLY TRIVIAL MANIFOLDS SUCH AS R4 SUGGESTS MANY EXCITING OPPORTUNITIES FOR APPLICATIONS OF POTENTIALLY DEEP IMPORTANCE FOR THE SPACETIME MODELS OF THEORETICAL PHYSICS, ESPECIALLY GENERAL RELATIVITY. THIS RICH PANOPLY OF NEW DIFFERENTIABLE STRUCTURES LIES IN THE PREVIOUSLY UNEXPLORED REGION BETWEEN TOPOLOGY AND GEOMETRY. JUST AS PHYSICAL GEOMETRY WAS THOUGHT TO BE TRIVIAL BEFORE EINSTEIN, PHYSICISTS HAVE CONTINUED TO WORK UNDER THE TACIT - BUT NOW SHOWN TO BE INCORRECT - ASSUMPTION THAT DIFFERENTIABILITY IS UNIQUELY DETERMINED BY TOPOLOGY FOR SIMPLE FOUR-MANIFOLDS. SINCE DIFFEOMORPHISMS ARE THE MATHEMATICAL MODELS FOR PHYSICAL COORDINATE TRANSFORMATIONS, EINSTEINS RELATIVITY PRINCIPLE REQUIRES THAT THESE MODELS BE PHYSICALLY INEQUIVALENT. THIS BOOK PROVIDES AN INTRODUCTORY SURVEY OF SOME OF THE RELEVANT MATHEMATICS AND PRESENTS PRELIMINARY RESULTS AND SUGGESTIONS FOR FURTHER APPLICATIONS TO SPACETIME MODELS.

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"... the authors have made a great effort to give enough details (being careful with definitions and with statements of theorems) so that the reader can get something more than the mere flavor of the subject ... References for all results are given throughout the book, and this may induce the interested reader to go more deeply into the subject."Mathematical Reviews"Readers who are willing to take this possibility into account will find this book most stimulating. I recommended it to everyone interested in the fundamentals of spacetime theory."General Relativity and Gravitation

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The recent revolution in differential topology related to the discovery of non-standard ("exotic") smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit - but now shown to be incorrect - assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models.

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Torsten Asselmeyer-Maluga
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ISBN 10: 981024195X ISBN 13: 9789810241957
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Descripción World Scientific Publishing Co Pte Ltd, 2001. HRD. Condición: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. del artículo: CA-9789810241957

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Torsten Asselmeyer-Maluga, Carl H. Brans
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Descripción World Scientific Publishing Co Pte Ltd, Singapore, 2007. Hardback. Condición: New. Language: English . Brand New Book. The recent revolution in differential topology related to the discovery of non-standard ( exotic ) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit - but now shown to be incorrect - assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein s relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models. Nº de ref. del artículo: AAJ9789810241957

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Torsten Asselmeyer-Maluga, Carl H. Brans
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Descripción World Scientific Publishing Co Pte Ltd, Singapore, 2007. Hardback. Condición: New. Language: English . Brand New Book. The recent revolution in differential topology related to the discovery of non-standard ( exotic ) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit - but now shown to be incorrect - assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein s relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models. Nº de ref. del artículo: AAJ9789810241957

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Torsten Asselmeyer-Maluga, Carl H. Brans
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Descripción World Scientific Publishing, 2007. Hardcover. Condición: New. Nº de ref. del artículo: DADAX981024195X

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Descripción World Scientific Publishing Co Pte Ltd. Hardback. Condición: new. BRAND NEW, Exotic Smoothness and Physics: Differential Topology and Spacetime Models, Torsten Asselmeyer-Maluga, Carl H. Brans, The recent revolution in differential topology related to the discovery of non-standard ("exotic") smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit - but now shown to be incorrect - assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models. Nº de ref. del artículo: B9789810241957

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Torsten Asselmeyer-Maluga, Carl H. Brans
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Descripción World Scientific Publishing Company, Inc. Condición: New. pp. 336. Nº de ref. del artículo: 7386605

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Descripción World Scientific Pub Co Inc, 2007. Hardcover. Condición: Brand New. 322 pages. 9.25x6.50x1.00 inches. In Stock. Nº de ref. del artículo: __981024195X

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Torsten Asselmeyer Maluga
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