Tamanoi Equation for Orbifold Euler Characteristics Revisited

Tamanoi equation is a Macdonald-type equation for the orbifold Euler characteristic and for its higher order analogs. It states that the generating series of fixed-order orbifold Euler characteristics of analogs of the symmetric powers for a space with a finite group action can be represented as a c...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2024-06, Vol.325 (1), p.111-119
Main Author: Gusein-Zade, S. M.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Analogs
Group theory
Mathematics
Mathematics and Statistics
Power series
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Summary:Tamanoi equation is a Macdonald-type equation for the orbifold Euler characteristic and for its higher order analogs. It states that the generating series of fixed-order orbifold Euler characteristics of analogs of the symmetric powers for a space with a finite group action can be represented as a certain unified (explicitly written) power series raised to the power equal to the orbifold Euler characteristic of the same order of the space itself. In the paper, in particular, we explain how the Tamanoi equation follows from its verification for actions of (finite) groups on the one-point space. We generalize the statements used for this purpose to analogs of the orbifold Euler characteristic corresponding to finitely generated groups. We show that, for these generalizations, an analog of the Tamanoi equation does not hold in general.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543824020068