Generalized twisted sectors of orbifolds

TL;DR

This paper introduces a unified framework for $ ext{Gamma}$-sectors of orbifolds, generalizing existing concepts like inertia orbifolds and multi-sectors, and explores their connections to fixed-point sectors and loop spaces.

Contribution

It establishes that $ ext{Gamma}$-sectors encompass various known sectors and provides a new model linking them to generalized loop spaces.

Findings

$ ext{Gamma}$-sectors unify inertia orbifolds and multi-sectors.

$ ext{Gamma}$-sectors are orbifold covers of fixed-point sectors.

The paper develops a model relating $ ext{Gamma}$-sectors to generalized loop spaces.

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.