Exotic Smoothness And Physics: Differential Topology And Spacetime Models - Hardcover

Asselmeyer-maluga, Torsten; Brans, Carl H

 
9789810241957: Exotic Smoothness And Physics: Differential Topology And Spacetime Models
Hardcover
ISBN 10: 981024195X ISBN 13: 9789810241957
Verlag: World Scientific Publishing Co Pte Ltd, 2007

Inhaltsangabe

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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Críticas

"... 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

Reseña del editor

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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Verlag
World Scientific Publishing Co Pte Ltd
Erscheinungsdatum
2007
Sprache
Englisch
ISBN 10 
981024195X
ISBN 13 
9789810241957
Einband
Tapa dura
Anzahl der Seiten
336
Kontakt zum Hersteller
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Verantwortliche Person
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