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Introduction to orbifolds
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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.
Forward citations
Cited by 3 Pith papers
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The complex projective plane as a ball quotient
The only ball-quotient structures on P^2 with smooth pairwise normal-crossing branch divisor are the Deligne–Mostow complete quadrilateral and the degree-9 dual Hesse arrangement.
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Diffeological Riemannian orbifolds
Riemannian metrics on orbifold stacks are equivalent to weak Riemannian metrics on the corresponding diffeological orbit spaces; regularity is necessary and properness is sufficient for the descent.
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Topological volumes of certain complete affine manifolds
Complete affine manifolds with an infinite amenable normal subgroup have amenable category at most their dimension, so all three topological volumes vanish.
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