Schmeding, Alexander: The diffeomorphism group of a non-compact orbifold. 2013
Content
- Acknowledgment
- Deutsche Zusammenfassung
- Introduction and statement of results
- 1 Preliminaries and Notation
- 1.1 Differential calculus in infinite dimensional spaces
- 1.2 Orbifolds I: Moerdijk's definition
- 1.3 Orbifolds II: Haefliger's definition
- 1.4 The topology of the base space of an orbifold
- 1.5 Local groups and the singular locus
- 1.6 Orbifold atlases with special properties
- 1.7 Examples of orbifolds
- 2 Maps of Orbifolds
- 2.1 Orbifold diffeomorphisms
- 2.2 Open suborbifolds and restrictions of orbifold maps
- 2.3 Partitions of unity for orbifolds
- 3 Tangent Orbibundles and their Sections
- 4 Riemannian Geometry on Orbifolds
- 5 Lie Group Structure on the Orbifold Diffeomorphism Group
- 5.1 Lie group structure on an identity neighborhood
- 5.2 Lie group structure on the orbifold diffeomorphism group
- 5.3 The Lie algebra
- 5.4 Regularity properties of the Diffeomorphismgroup
- 6 Application to Equivariant Diffeomorphism Groups
- A Hyperplanes and Paths in Euclidean Space
- B Group Actions and Newman`s Theorem
- C Infinite Dimensional Manifolds and Lie Groups
- C.1 Manifolds modeled on locally convex spaces
- C.2 Function spaces and their topologies
- C.3 Spaces of sections and patched spaces
- C.4 Lie groups
- C.5 Regular Lie groups
- D Riemannian Geometry: Supplementary Results
- E Maps of orbifolds
- E.1 (Quasi-)Pseudogroups
- E.2 Charted orbifold maps
- E.3 The identity morphism
- E.4 Composition of charted orbifold maps
- E.5 The orbifold category
- F Orbifold geodesics: Supplementary Results
- References
- List of Symbols
- List of Figures
- Index