Introduction to orbifolds

Abstract

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential Topology/Geometry, including orbibundles, differential forms, integration and (equivariant) De Rham cohomology; and Riemannian Geometry, surveying generalizations of classical theorems to this setting.

arXiv comment57 pages, 10 figures. Minor corrections

References in corpus (6)

• Differentiable Stacks and Gerbes
• Torus orbifolds, slice-maximal torus actions and rational ellipticity
• The diffeomorphism group of a non-compact orbifold
• Equivariant Alexandrov geometry and orbifold finiteness
• Orbifold finiteness under geometric and spectral constraints
• Equivariant basic cohomology under deformations

Cited by in corpus (3)

• Non arithmetic affine invariant orbifolds in Hodd(2, 2) and H(3, 1)
• On the Chabauty space of ${\text{PSL}}_2(\mathbb{R})$, I: lattices and grafting
• Leaf closures of Riemannian foliations: a survey on topological and geometric aspects of Killing foliations