On the existence of bibundles

Details On the existence of bibundles On the existence of bibundles

2011-02-22

arxiv.org/abs/1102.4388v2

Mathematics

Differential Geometry

This version accepted to appear in the Proceedings of the London Mathematical Society. Various changes made at referee's sugge

Scientific paper

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.

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