Generalized orbifold Euler characteristics for general orbifolds and wreath products

Abstract

We introduce the $\Gamma$-Euler-Satake characteristics of a general orbifold $Q$ presented by an orbifold groupoid $\mathcal{G}$, generalizing to orbifolds that are not necessarily 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 $\Gamma$-sectors of the orbifold where $\Gamma$ is a finitely generated discrete group. We study the behavior of these characteristics under product operations applied to the group $\Gamma$ 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 almost freely.

35 pages

References in corpus (6)

• Twisted Orbifold K-Theory
• Generalized Orbifold Euler Characteristic of Symmetric Products and Equivariant Morava K-Theory
• Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces
• Generalized twisted sectors of orbifolds
• Nonvanishing vector fields on orbifolds
• Two Gauss-Bonnet and Poincaré-Hopf Theorems for Orbifolds with Boundary

Cited by in corpus (4)

• Ab Initio Wall-Crossing
• Gauge-fixing on the Lattice via Orbifolding
• Orbifold Euler characteristics of non-orbifold groupoids
• Functional equations for orbifold wreath products