Generalized twisted sectors of orbifolds

Abstract

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

Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect

“…Orbifolds of A-sectors and inertia orbifolds. The Satake orbifold Euler characteristic and the string-theoretic orbifold Euler characteristic admit a family of common generalizations, see [66], [67] and in [27], [28], [29]. As above, let Y = X/G be a good orbifold.…”

$\Gamma $-extensions of the spectrum of an orbifold

“…If x ∈ M with isotropy group G x and ϕ : Γ → G x ≤ G is a homomorphism with image contained in G x , then a linear orbifold chart {V x , G x , π x } for O at the orbit Gx induces a linear orbifold chart V ϕ x , C Gx (ϕ), π ϕ x for O (ϕ) at the point C G (ϕ)x. Proposition 2.4 ( [14] and [15]). Let Γ be a finitely generated discrete group.…”

“…[14]). Let Γ be a finitely generated discrete group and let O be presented as a quotient orbifold G ⋉ M as above.…”

Classifying Closed 2-Orbifolds With Euler Characteristics

“…We denote the connected component of a homomorphism φ x : Γ → G x byQ (φ) . Note that the Z-sectors correspond to the inertia orbifold, and the F l -sectors correspond to the l-multi-sectors (see [8]; see also [1] or [5] for the definitions).…”