Generalized twisted sectors of orbifolds

Abstract

For a finitely generated discrete group $\Gamma$, the $\Gamma$-sectors of an orbifold $Q$ are a disjoint union of orbifolds corresponding to homomorphisms from $\Gamma$ into a groupoid presenting $Q$. Here, we show that the inertia orbifold and $k$-multi-sectors are special cases of the $\Gamma$-sectors, and that the $\Gamma$-sectors are orbifold covers of Leida's fixed-point sectors. In the case of a global quotient, we show that the $\Gamma$-sectors correspond to orbifolds considered by other authors for global quotient orbifolds as well as their direct generalization to the case of an orbifold given by a quotient by a Lie group. Furthermore, we develop a model for the $\Gamma$-sectors corresponding to a generalized loop space.

24 pages

References in corpus (7)

• Orbifolds as Groupoids: an Introduction
• Twisted Orbifold K-Theory
• Homotopy Theory of Orbispaces
• Generalized Orbifold Euler Characteristic of Symmetric Products and Equivariant Morava K-Theory
• Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces
• Nonvanishing vector fields on orbifolds
• Orbifolds and stable homotopy groups

Cited by in corpus (4)

• Generalized orbifold Euler characteristics for general orbifolds and wreath products
• Classifying closed 2-orbifolds with Euler characteristics
• Orbifold Euler characteristics of non-orbifold groupoids
• Functional equations for orbifold wreath products