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	Non disponible
ISBN 13	9781316514887
ISBN 10	1316514889
Titre	An Introduction to Infinite-Dimensional Differential Geometry
Auteur	Alexander Schmeding
Série	Cambridge Studies In Advanced Mathematics
État	Non disponible
Éditeur	Cambridge University Press
Année de publication	2022-12-22
Nombre de pages	280
Note de couverture	La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier.
Note	Non disponible