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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
3.1 The tangent orbifold and the tangent endofunctor
3.2 Orbisections
3.3 Spaces of orbisections
4 Riemannian Geometry on Orbifolds
4.1 Geodesics on orbifolds
4.2 The Riemannian orbifold exponential map
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
B.1 Group actions
B.2 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
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