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Mosc. Math. J., 2016, Volume 16, Number 4, Pages 751–765 (Mi mmj620)  

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

Equivariant versions of higher order orbifold Euler characteristics

S. M. Gusein-Zadea, I. Luengob, A. Melle-Hernándezb

a Moscow State University, Faculty of Mathematics and Mechanics, GSP-1, Moscow, 119991, Russia
b ICMAT (CSIC-UAM-UC3M-UCM); Complutense University of Madrid, Dept. of Algebra, Madrid, 28040, Spain

Abstract: There are (at least) two different approaches to define an equivariant analogue of the Euler characteristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach emerged from physics and includes the orbifold Euler characteristic and its higher order versions. Here we give a way to merge the two approaches together defining (in a certain setting) higher order Euler characteristics with values in the Burnside ring of a group. We give Macdonald type equations for these invariants. We also offer generalized (“motivic”) versions of these invariants and formulate Macdonald type equations for them as well.

Key words and phrases: finite group actions, orbifold Euler characteristic, Burnside ring, complex quasi-projective varieties, wreath products, generating series.

Funding Agency Grant Number
Russian Science Foundation 16-11-10018
Ministerio de Economía y Competitividad MTM2013-45710-C02-02-P
The work of the first named author (Sections 1, 2 and 4) was supported by the grant 16-11-10018 of the Russian Science Foundation. The second and third mentioned authors were supprted in part by the grant MTM2013-45710-C02-02-P.


DOI: https://doi.org/10.17323/1609-4514-2016-16-4-751-765

Full text: http://www.mathjournals.org/.../2016-016-004-010.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 55M35, 32Q55, 19A22
Received: June 5, 2016; in revised form June 30, 2016
Language:

Citation: S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Equivariant versions of higher order orbifold Euler characteristics”, Mosc. Math. J., 16:4 (2016), 751–765

Citation in format AMSBIB
\Bibitem{GusLueMel16}
\by S.~M.~Gusein-Zade, I.~Luengo, A.~Melle-Hern\'andez
\paper Equivariant versions of higher order orbifold Euler characteristics
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 4
\pages 751--765
\mathnet{http://mi.mathnet.ru/mmj620}
\crossref{https://doi.org/10.17323/1609-4514-2016-16-4-751-765}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3598506}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000391211000010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “The Universal Euler Characteristic of $V$-Manifolds”, Funct. Anal. Appl., 52:4 (2018), 297–307  mathnet  crossref  crossref  mathscinet  isi  elib
    3. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernandez, “Grothendieck ring of varieties with actions of finite groups”, Proc. Edinb. Math. Soc., 62:4 (2019), 925–948  crossref  mathscinet  zmath  isi  scopus
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