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Generalized orbifold
Euler characteristics for general orbifolds and wreath
products
Carla Farsi and Christopher Seaton |
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Algebraic & Geometric Topology 11 (2011) 523–551
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Abstract |
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We introduce the –Euler–Satake characteristics of a general orbifold presented by an orbifold groupoid , extending to orbifolds that are not global quotients the generalized orbifold Euler characteristics of Bryan–Fulman and Tamanoi. Each of these Euler characteristics is defined as the Euler–Satake characteristic of the space of –sectors of the orbifold where is a finitely generated discrete group. We study the behavior of these Euler characteristics under product operations applied to the group as well as the orbifold and establish their relationships to existing Euler characteristics for orbifolds. As applications, we generalize formulas of Tamanoi, Wang and Zhou for the Euler characteristics and Hodge numbers of wreath symmetric products of global quotient orbifolds to the case of quotients by compact, connected Lie groups acting locally freely, in particular including all closed, effective orbifolds. |
Keywords
orbifold, wreath product, Euler–Satake characteristic,
orbifold Euler characteristic, orbifold Hodge number
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Mathematical Subject Classification 2000
Primary: 22A22, 55S15
Secondary: 58E40, 55N91
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References |
Publication
Received: 11 December 2009
Revised: 3 December 2010
Accepted: 6 December 2010
Published: 15 February 2011
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Authors |
| Carla Farsi | |
| Department of Mathematics University of Colorado at Boulder Campus Box 395 Boulder CO 80309-0395 USA |
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| http://www.colorado.edu/math/people/professors/farsi.html | |
| Christopher Seaton | |
| Department of Mathematics and
Computer Science Rhodes College 2000 North Parkway Memphis TN 38112-1690 USA |
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| http://faculty.rhodes.edu/seaton/ | |
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