Inertia Orbifolds, Configuration Spaces and the Ghost Loop Space

E. Lupercio
2004 Quarterly Journal of Mathematics  
In this paper we define and study the ghost loop orbifold L s X of an orbifold X consisting of those loops that remain constant in the coarse moduli space of X. We construct a configuration space model for L s X using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cyclic homologies of the inertia orbifold of X (that generate the so-called twisted sectors in string theory) and the ordinary and equivariant homologies of L s X. We also show how this clarifies the
more » ... this clarifies the relation between Chen-Ruan orbifold cohomology, Hochschild homology, and periodic cyclic homology. We dedicate this paper to Professor Graeme B. Segal on the occasion of his 60th Birthday †
doi:10.1093/qmath/hag053 fatcat:rxmvyzzlnnaedhzpevzgppsncm