Geometry in a Fréchet Context A Projective Limit Approach

Dodson, CTJ and Galanis, G and Vassiliou, E (2015) Geometry in a Fréchet Context A Projective Limit Approach. LMS Lecture Notes in Mathematics, 428 . Cambridge University Press, Cambridge, UK. ISBN 9781316601952 (In Press)

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Abstract

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. 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.

Item Type:	Book
Additional Information:	This link is to the Table of Contents and Preface: http://www.maths.manchester.ac.uk/~kd/PREPRINTS/FrechetGeometryContents.pdf
Uncontrolled Keywords:	Banach manifold, Fréchet manifold, bundles, projective limits, connection, curvature, differential equations
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User:	Prof CTJ Dodson
Date Deposited:	30 Nov 2015
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2416

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