Alzaareer, Hamza: Lie groups of mappings on non-compact spaces and manifolds. 2013
Inhalt
- 1 Introduction
- 2 Preliminaries
- 2.1 Differential calculus in locally convex spaces
- 2.2 Manifolds
- 2.3 Infinite-dimensional Lie groups and their Lie algebras
- 2.4 Spaces of mappings
- 3 Cr,s-mappings
- 3.1 Elementary properties
- 3.2 Chain Rules for Cr,s-mappings
- 3.3 The Exponential Law for Cr,s-mappings
- 3.4 The Exponential Law for Cr,s-mappings on manifolds
- 4 Calpha
- 4.1 Elementary properties
- 4.2 Chain Rule for C-mappings
- 4.3 The Exponential Law for C-mappings
- 4.4 The Exponential Law for C-mappings on manifolds
- 5 Regular Lie groups and the Fundamental Theorem
- 6 The mapping group as an infinite-dimensional Lie group
- 7 Lie group structures on weighted function spaces
- 7.1 Weighted function spaces
- 7.2 Weighted topological Lie algebras
- 7.3 The Lie group structure on CV(X,H)
- 7.4 Weighted Lie algebras and continuous product
- Bibliography