English

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 XX consisting of those loops that remain constant in the coarse moduli space of XX. 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 XX (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}
}