Abstract

For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has the same cohomology as M. The use of S(M) in explicit calculations is illustrated in the example of the `teardrop' orbifold. Introduction. Orbifolds or V-manifolds were first introduced by Satake [9], and arise naturally in many ways. For example, the orbit space of any proper action by a (discrete) group on a manifold has the structure of an orbifold; this applies in particular to moduli spaces. Furthermore, the orbit space of any almost free action by a compact Lie group has the structure of an orbifold, as does the leaf space of any foliation with compact leaves and finite holonomy. Examples of orbifolds are discussed in [3, 9, 11] and many others. For an orbifold M, one can define in a natural way a cohomology theory with coefficients in any l...

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