Geometry in a Fréchet contex : a projective limit approach / C.T.J. Dodson, University of Manchester, George Galanis, Hellenic Naval Academy, Piraeus, Greece, Efstathios Vassiliou, University of Athens, Greece.

By:

Dodson, C. T. J [author.]

Contributor(s):

Material type: Text

TextSeries: London Mathematical Society lecture note series ; 428.Publisher: Cambridge : Cambridge University Press, 2016Description: 1 online resource (xii, 302 pages) : digital, PDF file(s)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781316556092 (ebook)

Subject(s):

Additional physical formats: Print version: : No titleDDC classification:

515/.732 23

LOC classification:

QA322 .D63 2016

Online resources:

Click here to access online

Summary: 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.

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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.

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National Science Library of Georgia

Geometry in a Fréchet contex : a projective limit approach / C.T.J. Dodson, University of Manchester, George Galanis, Hellenic Naval Academy, Piraeus, Greece, Efstathios Vassiliou, University of Athens, Greece.