Geodesic
The Universal Euler Characteristic of $V$-Manifolds
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 72-85.

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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 ${\mathbb Z}$-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.
Mots-clés : finite group actions
Keywords: $V$-manifold, orbifold, additive topological invariant, lambda-ring, Macdonald identity. 
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S. M. Gusein-Zade; I. Luengo; A. Melle-Hernández. The Universal Euler Characteristic of $V$-Manifolds. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 72-85. http://geodesic.mathdoc.fr/item/FAA_2018_52_4_a4/

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