Algebraic & Geometric Topology

Generalized orbifold Euler characteristics for general orbifolds and wreath products

Carla Farsi and Christopher Seaton

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We introduce the Γ–Euler–Satake characteristics of a general orbifold Q presented by an orbifold groupoid G, 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 Γ–sectors of the orbifold where Γ is a finitely generated discrete group. We study the behavior of these Euler characteristics under product operations applied to the group Γ 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.

Article information

Algebr. Geom. Topol., Volume 11, Number 1 (2011), 523-551.

Received: 11 December 2009
Revised: 3 December 2010
Accepted: 6 December 2010
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 55S15: Symmetric products, cyclic products
Secondary: 58E40: Group actions 55N91: Equivariant homology and cohomology [See also 19L47]

orbifold wreath product Euler–Satake characteristic orbifold Euler characteristic orbifold Hodge number


Farsi, Carla; Seaton, Christopher. Generalized orbifold Euler characteristics for general orbifolds and wreath products. Algebr. Geom. Topol. 11 (2011), no. 1, 523--551. doi:10.2140/agt.2011.11.523.

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