Geometry in a Fréchet Context: A Projective Limit Approach

London Mathematical Society Lecture Note #428

by C.T.J. Dodson, George Galanis, Efstathios Vassiliou

Many geometrical features of manifolds and fibre bundles modelled on Fr�chet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fr�chet 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 Fr�chet space, and the non-existence of an exponential map in a Fr�chet-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.

314 pages, Kindle Edition

First published November 30, 2015