Geometry in a Frechet Context: A Projective Limit Approach

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. Features: Proposes a new approach that overcomes many complications of the geometric theory. Self-contained chapters and detailed proofs help the reader progress systematically through the book. Includes an extensive introduction to the geometry of Banach manifolds and bundles. Provides a number of suggestions for further research in the geometry and for applications, notably in physical field theory.