What is the "right" analog in the orbifold case of a singular homology of a topological space? We can not just take the homology of the underlying space, because it does not contain much imformation. For example, is there any kind homology of orbifold such that the first homology is abelien of the fundamental group of the orbifold? And a n dim orbifold will have all homology group higher than n dim equal to zero? And if there is such a homology, will there be Poincare duality in the orbifold case???

Thanks very much!

What is the "right" analog in the orbifold case of a singular homology of a topological space? We can not just take the homology of the underlying space, because it does not contain much information. For example, is there any kind homology of orbifolds such that the first homology group is the abelianization of the fundamental group of the orbifold? And such that an $n$-dim orbifold will have all homology group higher than $n$-dim equal to zero? And if there is such a homology, will there be Poincare duality in the orbifold case???

Thanks very much!