Generalized twisted sectors of orbifolds

Carla Farsi and Christopher Seaton

Vol. 246 (2010), No. 1, 49–74

DOI: 10.2140/pjm.2010.246.49

Abstract

For a finitely generated discrete group Γ, the Γ-sectors of an orbifold Q are a disjoint union of orbifolds corresponding to homomorphisms from Γ into a groupoid presenting Q. Here, we show that the inertia orbifold and k-multisectors are special cases of the Γ-sectors, and that the Γ-sectors are orbifold covers of Leida’s fixed-point sectors. In the case of a global quotient, we show that the Γ-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 Γ-sectors corresponding to a generalized loop space.

Keywords

orbifold, orbifold groupoid, twisted sector, loop groupoid

Mathematical Subject Classification 2000

Primary: 22A22, 57S15

Secondary: 57S17, 58H05

Milestones

Received: 6 March 2009

Accepted: 3 December 2009

Published: 1 May 2010