Functional Analysis and Its Applications

, Volume 52, Issue 4, pp 297–307 | Cite as

The Universal Euler Characteristic of V-Manifolds

  • S. M. Gusein-ZadeEmail author
  • I. Luengo
  • A. Melle-Hernández


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.

Key words

finite group actions V-manifold orbifold additive topological invariant lambda-ring Macdonald identity 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • S. M. Gusein-Zade
    • 1
    Email author
  • I. Luengo
    • 2
    • 3
  • A. Melle-Hernández
    • 4
  1. 1.Moscow State University, Faculty of Mechanics and MathematicsMoscowRussia
  2. 2.ICMAT, Madrid, Spain Department of Algebra, Geometry, and TopologyComplutense University of MadridMadridSpain
  3. 3.ICMATMadridSpain
  4. 4.Institute of Interdisciplinary Mathematics, Department of Algebra, Geometry, and TopologyComplutense University of MadridMadridSpain

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