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

This article is cited in 3 scientific papers (total in 3 papers)

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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\by S.~M.~Gusein-Zade, I.~Luengo, A.~Melle-Hern\'andez
\paper The Universal Euler Characteristic of $V$-Manifolds
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 4
\pages 72--85
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\pages 297--307
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Cibotaru D., Moroianu S., “Odd Pfaffian Forms”, Bull. Braz. Math. Soc.  crossref  isi  scopus
    2. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernandez, “Generalized orbifold Euler characteristics on the Grothendieck ring of varieties with actions of finite groups”, Symmetry-Basel, 11:7 (2019), 902  crossref  mathscinet  isi
    3. S. M. Gusein-Zade, “Indeks osoboi tochki vektornogo polya ili $1$-formy na orbifolde”, Algebra i analiz, 33:3 (2021), 73–84  mathnet
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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