Loop Groupoids, Gerbes, and Twisted Sectors on Orbifolds
arXiv:math/0110207
Abstract
The purpose of this paper is to introduce the notion of loop groupoid associated to a groupoid. After studying the general properties of the loop groupoid, we show how this notion provides a very natural geometric interpretation for the twisted sectors of an orbifold, and for the inner local systems introduced by Ruan by means of a natural generalization of the concept holonomy of a gerbe.
Revised version. 23 pages. To appear in "Madison Orbifolds", Contemp. Math