Alexander Schmeding (Norway Nord Universitet)

An Introduction to Infinite-Dimensional Differential Geometry

• Gebundenes Buch

Produktbeschreibung

This text introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, exploring modern applications. Emphasising connections to finite-dimensional geometry, it is accessible to graduate students, as well as researchers wishing to learn about the subject. Also available as Open Access on Cambridge Core.

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Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• Seitenzahl: 280
• Erscheinungstermin: 22. Dezember 2022
• Englisch
• Abmessung: 229mm x 152mm x 19mm
• Gewicht: 582g
• ISBN-13: 9781316514887
• ISBN-10: 1316514889
• Artikelnr.: 63939242

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.