An Introduction to Infinite-Dimensional Differential Geometry (Cambridge Studies in Advanced Mathematics, Series Number 202) - Hardcover

Schmeding, Alexander

Hardcover

ISBN 10: 1316514889 ISBN 13: 9781316514887

Publisher: Cambridge University Press, 2022

Synopsis

Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

About this title

About the Author

Alexander Schmeding is Associate Professor in Mathematics at Nord University at Levanger.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2022
• Language: English
• ISBN 10: 1316514889
• ISBN 13: 9781316514887
• Binding: Hardcover
• Edition number: 1
• Number of pages: 280