The Universal Euler Characteristic of V-Manifolds

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 -ma...

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Bibliographic Details
Published in:Functional analysis and its applications 2018-10, Vol.52 (4), p.297-307
Main Authors: Gusein-Zade, S. M., Luengo, I., Melle-Hernández, A.
Format: Article
Language:English
Subjects:
Analysis
Functional Analysis
Invariants
Isomorphism
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-018-0239-y