An Introduction to Infinite-Dimensional Differential Geometry by Alexander Schmeding

An Introduction to Infinite-Dimensional Differential Geometry by Alexander Schmeding

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.

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

SKU	Unavailable
ISBN 13	9781316514887
ISBN 10	1316514889
Title	An Introduction to Infinite-Dimensional Differential Geometry
Author	Alexander Schmeding
Series	Cambridge Studies In Advanced Mathematics
Condition	Unavailable
Publisher	Cambridge University Press
Year published	2022-12-22
Number of pages	280
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable