Geometry in a Fréchet context : a projective limit approach
Author(s)
Bibliographic Information
Geometry in a Fréchet context : a projective limit approach
（London Mathematical Society lecture note series, 428）
Cambridge University Press, 2016
- : pbk
Available at 39 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkS||LMS||428200033912528
Note
Includes bibliographical references (p. 281-290) and index
Description and Table of Contents
Description
Many geometrical features of manifolds and fibre bundles modelled on Frechet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Frechet 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 Frechet space, and the non-existence of an exponential map in a Frechet-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.
Table of Contents
- Preface
- 1. Banach manifolds and bundles
- 2. Frechet spaces
- 3. Frechet 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.
by "Nielsen BookData"