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
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.
|Russian Science Foundation
|Ministerio de Economía y Competitividad
|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.
MSC: 55M35, 32Q55, 19A22
Received: June 5, 2016; in revised form June 30, 2016
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
\by S.~M.~Gusein-Zade, I.~Luengo, A.~Melle-Hern\'andez
\paper Equivariant versions of higher order orbifold Euler characteristics
\jour Mosc. Math.~J.
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This publication is cited in the following articles:
S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “The Universal Euler Characteristic of $V$-Manifolds”, Funct. Anal. Appl., 52:4 (2018), 297–307
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
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