An Introduction to Infinite-Dimensional Differential Geometry Schmeding Alexander
An Introduction to Infinite-Dimensional Differential Geometry Schmeding Alexander Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is…
Specifikacia An Introduction to Infinite-Dimensional Differential Geometry Schmeding Alexander
An Introduction to Infinite-Dimensional Differential Geometry Schmeding Alexander
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. 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.
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. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate
Differential Geometry