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This article is cited in 4 scientific papers (total in 4 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.
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
Linking options:
https://www.mathnet.ru/eng/faa3595https://doi.org/10.4213/faa3595 https://www.mathnet.ru/eng/faa/v52/i4/p72
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Abstract page: | 382 | Full-text PDF : | 61 | References: | 36 | First page: | 18 |
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