Frontmatter
Contents
Preface
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: PDEs via Geometry
8 The Geometry of Rough Paths
Appendix A A Primer on Topological Vector Spaces and Locally Convex Spaces
Appendix B Basic Ideas from Topology
Appendix C Canonical Manifold of Mappings
Appendix D Vector Fields and Their Lie Bracket
Appendix E Differential Forms on Infinite-Dimensional Manifolds
Appendix F Solutions to Selected Exercises
References
Index

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Type: Chapter
Information: An Introduction to Infinite-Dimensional Differential Geometry , pp. v - vi

DOI: https://doi.org/10.1017/9781009091251 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2022
Creative Commons: This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/cclicenses/

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