Cutting and pasting of manifolds into G-manifolds

抄録

If we are given a G-manifold M, G a finite abelian group of odd order, by taking fixed submanifolds M^H for various subgroups H of G, we obtain a family (M^H)_H≤G of submanifolds of M. The Euler characteristics χ(M^H) of such submanifolds satisfy some congruence relations. Conversely, in this paper we show that if we are given a family (N_i) of submanifolds N_i of a manifold N and if the Euler characteristics χ(N_i) satisfy some congruence relations, then, after adding some family, (N_i) can be cut and pasted into a family obtained from a G-manifold.