Inertia Orbifolds, Configuration Spaces and the Ghost Loop Space
Algebraic Topology
2007-05-23 v2 Geometric Topology
Abstract
In this paper we define and study the "ghost loop orbifold" of an orbifold consisting of those loops that remain constant in the coarse moduli space of . We construct a configuration space model for the ghost loop orbifold using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cyclic homologies of the inertia orbifold of (that generate the so-called twisted sectors in string theory) and the ordinary and equivariant homologies of the ghost loop orbifold. We also show how this clarifies the relation between orbifold K-theory, Chen-Ruan orbifold cohomology, Hochschild homology, and periodic cyclic homology.
Cite
@article{arxiv.math/0210222,
title = {Inertia Orbifolds, Configuration Spaces and the Ghost Loop Space},
author = {Ernesto Lupercio and Bernardo Uribe},
journal= {arXiv preprint arXiv:math/0210222},
year = {2007}
}