Alexander Schmeding

Introduction to Infinite-Dimensional Differential Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 22. Dezember 2022
• Englisch
• ISBN-13: 9781009089302
• Artikelnr.: 70912382

Autorenporträt

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

Inhaltsangabe

1. Calculus in locally convex spaces
2. Spaces and manifolds of smooth maps
3. Lifting geometry to mapping spaces I: Lie groups
4. Lifting geometry to mapping spaces II: (weak) Riemannian metrics
5. Weak Riemannian metrics with applications in shape analysis
6. Connecting finite-dimensional, infinite-dimensional and higher geometry
7. Euler-Arnold theory: PDE via geometry
8. The geometry of rough paths
A. A primer on topological vector spaces and locally convex spaces
B. Basic ideas from topology
C. Canonical manifold of mappings
D. Vector fields and their Lie bracket
E. Differential forms on infinite-dimensional manifolds
F. Solutions to selected exercises
References
Index.