An Introduction to Infinite-Dimensional Differential Geometry

ISBN-13: 9781316514887 / Angielski / Twarda / 2022 / 280 str.

Alexander Schmeding

Opis

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

Spis treści

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.