Geometry in a Fréchet Context: A Projective Limit Approach (London Mathematical Society Lecture Note Series, Series Number 428)

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. Aimed at researchers and graduate students, this book presents a new approach to studying Fréchet geometry which overcomes deficiencies of the Fréchet 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. 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. C.t.j. Dodson, University Of Manchester, Uk, George Galanis, Hellenic Naval Academy, Piraeus, Greece, Efstathios Vassiliou, University Of Athens, Greece. Includes Bibliographical References And Index.