Simplicial Cohomology of Orbifolds

Abstract

For any orbifoldM, we explicitly construct a simplicial complex S(M) from a given triangulation of the ‘coarse’ underlying space together with the local isotropy groups ofM. We prove that, for any local system onM, 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.