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An Introduction to Infinite-Dimensional Differential Geometry (Hardcover)
Loot Price: R1,681
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An Introduction to Infinite-Dimensional Differential Geometry (Hardcover)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 17 working days
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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.
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