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London Mathematical Society Lecture Note Series.Geometry in a Frechet Context: A Projective Limit Approach

  • Kartonierter Einband
  • 314 Seiten
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Informationen zum Autor C. T. J. Dodson is Emeritus Professor of Mathematics at the University of Manchester. Many geometrical fe... Weiterlesen
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Beschreibung

Informationen zum Autor C. T. J. Dodson is Emeritus Professor of Mathematics at the University of Manchester. Klappentext Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fréchet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Fréchet space, and the non-existence of an exponential map in a Fréchet-Lie group. In this book, the authors describe in detail a new approach that overcomes many of these limitations by using projective limits of geometrical objects modelled on Banach spaces. It will appeal to researchers and graduate students from a variety of backgrounds with an interest in infinite-dimensional geometry. The book concludes with an appendix outlining potential applications and motivating future research. Zusammenfassung Aimed at researchers and graduate students, this book presents a new approach to studying Frechet geometry which overcomes deficiencies of the Frechet space theory, such as the lack of a general solvability theory for differential equations. The book concludes with a series of open problems and suggestions for further research. Inhaltsverzeichnis Preface; 1. Banach manifolds and bundles; 2. Fréchet spaces; 3. Fréchet manifolds; 4. Projective systems of principal bundles; 5. Projective systems of vector bundles; 6. Examples of projective systems of bundles; 7. Connections on plb-vector bundles; 8. Geometry of second order tangent bundles; Appendix. Further study.

Autorentext

C. T. J. Dodson is Emeritus Professor of Mathematics at the University of Manchester.



Klappentext

Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fréchet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Fréchet space, and the non-existence of an exponential map in a Fréchet-Lie group. In this book, the authors describe in detail a new approach that overcomes many of these limitations by using projective limits of geometrical objects modelled on Banach spaces. It will appeal to researchers and graduate students from a variety of backgrounds with an interest in infinite-dimensional geometry. The book concludes with an appendix outlining potential applications and motivating future research.



Zusammenfassung
Aimed at researchers and graduate students, this book presents a new approach to studying Frechet geometry which overcomes deficiencies of the Frechet space theory, such as the lack of a general solvability theory for differential equations. The book concludes with a series of open problems and suggestions for further research.

Inhalt

Preface; 1. Banach manifolds and bundles; 2. Fréchet spaces; 3. Fréchet manifolds; 4. Projective systems of principal bundles; 5. Projective systems of vector bundles; 6. Examples of projective systems of bundles; 7. Connections on plb-vector bundles; 8. Geometry of second order tangent bundles; Appendix. Further study.

Produktinformationen

Titel: London Mathematical Society Lecture Note Series.Geometry in a Frechet Context: A Projective Limit Approach
Untertitel: A Projective Limit Approach
Autor:
EAN: 9781316601952
ISBN: 978-1-316-60195-2
Format: Kartonierter Einband
Herausgeber: Cambridge University Press
Genre: Mathematik
Anzahl Seiten: 314
Gewicht: 462g
Größe: H228mm x B154mm x T21mm
Jahr: 2015

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