An introduction to infinite-dimensional differential geometry
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 t...
| Otros Autores: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge, United Kingdom ; New York, NY :
Cambridge University Press
2023.
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| Edición: | First edition |
| Colección: | Cambridge studies in advanced mathematics ;
202. |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009769414306719 |
Tabla de Contenidos:
- 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.
