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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 4, Pages 72–85 (Mi faa3595)  

The Universal Euler Characteristic of $V$-Manifolds

S. M. Gusein-Zadea, I. Luengobc, A. Melle-Hernándezd

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute of Mathematical Sciences, Madrid
c Departamento de Álgebra, Universidad Complutense de Madrid
d Institute of Interdisciplinary Mathematics, Department of Algebra, Geometry, and Topology, Complutense University of Madrid

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 ${\mathbb Z}$-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.

Keywords: finite group actions, $V$-manifold, orbifold, additive topological invariant, lambda-ring, Macdonald identity.

Funding Agency Grant Number
Russian Science Foundation 16-11-10018
Ministerio de Economía y Competitividad MTM2016-76868-C2-1-P


DOI: https://doi.org/10.4213/faa3595

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English version:
Functional Analysis and Its Applications, 2018, 52:4, 297–307

Bibliographic databases:

UDC: 515.165
Received: 06.06.2018

Citation: S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “The Universal Euler Characteristic of $V$-Manifolds”, Funktsional. Anal. i Prilozhen., 52:4 (2018), 72–85; Funct. Anal. Appl., 52:4 (2018), 297–307

Citation in format AMSBIB
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\paper The Universal Euler Characteristic of $V$-Manifolds
\jour Funktsional. Anal. i Prilozhen.
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\vol 52
\issue 4
\pages 72--85
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