Articles
On the existence of bibundles
2010 Mathematics Subject Classification 55R65 (primary), 53C08, 18D05 (secondary).
The first author acknowledges the support of the Australian Research Council. The second author acknowledges the support of an Australian Postgraduate Research Award. The third author was supported by the Engineering and Physical Sciences Research Council [grant number EP/I010610/1].
Abstract
We consider the existence of bibundles, in other words locally trivial principal G spaces with commuting left and right G actions. We show that their existence is closely related to the structure of the group Out(G) of outer automorphisms of G. We also develop a classifying theory for bibundles. The theory is developed in full generality for (H, G) bibundles for a crossed module (H, G) and we show with examples the close links with loop group bundles.
