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. 
@article{FAA_2018_52_4_a4,
     author = {S. M. Gusein-Zade and I. Luengo and A. Melle-Hern\'andez},
     title = {The {Universal} {Euler} {Characteristic} of $V${-Manifolds}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {72--85},
     publisher = {mathdoc},
     volume = {52},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_4_a4/}
}
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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/