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.
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Translated from Funktsional′nyi Analiz i Ego Prilozheniya, Vol. 52, No. 4, pp. 72–85, 2018
The work of the first author (Sections 2, 5, and 6) was supported by the Russian Science Foundation, grant 16-11-10018. The work of the second and third authors was partially supported by the competitive Spanish national grant MTM2016-76868-C2-1-P.
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Gusein-Zade, S.M., Luengo, I. & Melle-Hernández, A. The Universal Euler Characteristic of V-Manifolds. Funct Anal Its Appl 52, 297–307 (2018). https://doi.org/10.1007/s10688-018-0239-y
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DOI: https://doi.org/10.1007/s10688-018-0239-y