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Higher-order orbifold Euler characteristics for compact Lie group actions

Part of: Operations and obstructions

Published online by Cambridge University Press:  26 November 2015

S. M. Gusein-Zade ,
I. Luengo  and
A. Melle-Hernández
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Abstract

We generalize the notions of the orbifold Euler characteristic and of the higher-order orbifold Euler characteristics to spaces with actions of a compact Lie group using integration with respect to the Euler characteristic instead of the summation over finite sets. We show that the equation for the generating series of the kth-order orbifold Euler characteristics of the Cartesian products of the space with the wreath products actions proved by Tamanoi for finite group actions and by Farsi and Seaton for compact Lie group actions with finite isotropy subgroups holds in this case as well.

Keywords

compact Lie group actionsorbifold Euler characteristicwreath productsgenerating seriescompact Lie group actions

MSC classification

Secondary: 57S10: Compact groups of homeomorphisms 55S15: Symmetric products, cyclic products
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 6 , December 2015 , pp. 1215 - 1222
Copyright
Copyright © Royal Society of Edinburgh 2015 

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