# The Universal Euler Characteristic of *V*-Manifolds

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## Abstract

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with certain finiteness properties. A generalization of the notion of a manifold is the notion of a *V*-manifold. We discuss a universal additive topological invariant of *V*-manifolds, the universal Euler characteristic. It takes values in the ring freely generated (as a Z-module) by isomorphism classes of finite groups. We also consider the universal Euler characteristic on the class of locally closed equivariant unions of cells in equivariant CW-complexes. We show that it is a universal additive invariant satisfying a certain “induction relation.” We give Macdonald-type identities for the universal Euler characteristic for *V*-manifolds and for cell complexes of the described type.

## Key words

finite group actions*V*-manifold orbifold additive topological invariant lambda-ring Macdonald identity

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