An Introduction to Infinite-Dimensional Differential Geometry (Hardcover)

Alexander Schmeding

ISBN 10: 1316514889 / ISBN 13: 9781316514887

Published by Cambridge University Press, Cambridge, 2022

About this Item

Hardcover. 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. This text introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, exploring modern applications. Emphasising connections to finite-dimensional geometry, it is accessible to graduate students, as well as researchers wishing to learn about the subject. Also available as Open Access on Cambridge Core. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9781316514887

Bibliographic Details

• Title: An Introduction to Infinite-Dimensional Differential Geometry (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2022
• Language: English
• ISBN 10: 1316514889
• ISBN 13: 9781316514887
• Binding: Hardcover
• Condition: new

About this title

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 the Author

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