The first homology of the group of equivariant diffeomorphisms and its applications

Let V be a representation space of a finite group G. We determinethe group structure of the first homology of the equivariantdiffeomorphism group of V. Then we can apply it to the calculationof the first homology of the corresponding automorphism groupsof smooth orbifolds, compact Hausdorff foliations, codimensionone or two compact foliations and the locally free S¹-actionson 3-manifolds. Received November 5, 2007.