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On Noncommutative Geometry of Orbifolds (1405.7139v4)
Published 28 May 2014 in math.DG, math-ph, math.MP, and math.OA
Abstract: An orbifold is a Morita equivalence class of a proper {\' e}tale Lie groupoid. A unitary equivalence class of spectral triples over the algebra of smooth invariant functions are associated with any compact spin orbifold. In the case of an effective spin orbifold we construct a collection of spectral triples over the smooth convolution algebras of the representatives of the Morita equivalence class.