An Introduction to Infinite-Dimensional Differential Geometry / Alexander Schmeding  

Public ISBD Titre : An Introduction to Infinite-Dimensional Differential Geometry Type de document : document électronique Auteurs : Alexander Schmeding, Auteur Editeur : Cambridge [United Kingdom] : Cambridge University Press Année de publication : 2022 Importance : 284 p. Présentation : ill. ISBN/ISSN/EAN : 978-1-00-909125-1 Langues : Anglais (eng) Tags : Geometry  Differential Geometry  Infinite-dimensional manifolds  Frechet spaces  Hilbert manifolds  Banach manifolds  Lie groups  Diffeomorphism groups  Loop spaces  Tangent bundles  Riemannian metrics  Global analysis Index. décimale : 516 Géométrie Résumé : 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. En ligne : https://doi.org/10.1017/9781009091251 An Introduction to Infinite-Dimensional Differential Geometry [document électronique] / Alexander Schmeding, Auteur . - Cambridge (United Kingdom) : Cambridge University Press, 2022 . - 284 p. : ill. ISBN : 978-1-00-909125-1 Langues : Anglais (eng) Tags : Geometry  Differential Geometry  Infinite-dimensional manifolds  Frechet spaces  Hilbert manifolds  Banach manifolds  Lie groups  Diffeomorphism groups  Loop spaces  Tangent bundles  Riemannian metrics  Global analysis Index. décimale : 516 Géométrie Résumé : 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. En ligne : https://doi.org/10.1017/9781009091251

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