Direct and Projective Limits of Geometric Banach Structures.
- 472 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Direct and Projective Limits of Geometric Banach Structures.
About this book
This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced.
Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics.
This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.
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Information
Table of contents
- Cover Page
- Half-Title Page
- Series Page
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- Authors
- Acknowledgements
- List of Figures
- 1 Preliminaries
- 2 Banach-Lie Structures
- 3 Convenient Structures
- 4 Projective Limits
- 5 Direct Limits
- 6 Convenient Lie Algebroids and Prolongations
- 7 Partial Poisson Structures
- 8 Integrability of Distributions
- A Fréchet Spaces
- B Categories
- C Sheaves Theory
- D Locally Convex Vector Bundles
- E The KdV Equation
- F Formal Integrability of Systems of PDEs
- Further Studies
- Bibliography
- Index